Remaining Poor or Growing at a High Rate: a Sectoral Analysis · Author: Belen Inguanzo Lorenzo´...

Remaining Poor or Growing at a High Rate:a Sectoral Analysis

Author: Belen Inguanzo LorenzoSupervisor: Amaia Iza Padilla

Abstract. This paper shows how affects the productivity growth in each sector to the evolutionof the aggregate productivity and the income per capita of the poorest countries. Given the sec-toral data available, the analysis is based on 9 countries for the period 1975 − 2010. In orderto determine the sectors leading their evolution, we construct a model that allows us to answerwhat would have happened if they had followed a distinct sectoral productivity path. We find thatagriculture and personal and government services are sectors influencing greatly in the relativeaggregate productivity and income per capita growth of countries. In addition, we observe that theproductivity growth in manufacturing has been important for the countries that moved either to ahigher quintile or became poorer. However, the productivity growth in trade services was relevantfor the countries that remained in the lowest quintile or fell to it. In general, experiencing thesectoral productivity path of countries with a higher increase in income per capita, would haveincreased the relative aggregate productivity and income per capita of countries with respect tothat observed.Keywords. Income per capita, productivity, quintile.

Master Thesis, 2016− 2017.Master in Economics: Empirical Applications and PoliciesUniversidad del Paıs Vasco - Euskal Herriko Unibersitatea

Contents

1 Introduction 1

2 Description of data 42.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3 Observed facts 7

4 The model 214.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.3 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.3.1 Simulation of the sectoral shares of employment . . . . . . . . . . . . . . . . . 314.3.2 Simulation of the relative aggregate productivity and the income per capita

of countries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.4 Evaluation of the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5 Counterfactuals 385.1 Role of the sectoral productivity growth of countries in their relative aggregate pro-

ductivity and income per capita . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385.2 The importance of specific sectoral productivity paths . . . . . . . . . . . . . . . . . . 40

6 Conclusions 43

A The decision problem of households 46

B Market clearing conditions 51

C Counterfactuals: changes in the sectoral shares of employment 53

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List of Figures

3.1 GDP per capita evolution by groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2 GDP per capita evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.3 Aggregate productivity evolution by groups . . . . . . . . . . . . . . . . . . . . . . . . 133.4 Aggregate productivity evolution within groups . . . . . . . . . . . . . . . . . . . . . 143.5 Sectoral share of labor by groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.1 Comparison between the simulated and the observed sectoral shares of labor . . . . 334.2 Comparison between the simulated and the observed changes in sectoral shares of

labor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

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List of Tables

3.1 Bounds and range of the quintiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.2 Poorest countries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.3 Average annual growth rate of the income per capita . . . . . . . . . . . . . . . . . . 103.4 Aggregate productivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.5 Average annual growth rates of the sectoral productivity . . . . . . . . . . . . . . . . 153.6 Sectoral share of labor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.7 Comparison of the sectoral shares of labor . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.1 Calibration of parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.2 Estimated sectoral productivity levels in 1975 . . . . . . . . . . . . . . . . . . . . . . . 304.3 Average annual growth of sectoral productivity(%) . . . . . . . . . . . . . . . . . . . . 304.4 Statistics to evaluate the performance of the model . . . . . . . . . . . . . . . . . . . 36

5.1 Importance of the sectoral productivity growth in the evolution of countries . . . . . 395.2 Consequences of following specific sectoral productivity paths . . . . . . . . . . . . . 41

iii

Chapter 1

Introduction

Most countries have experienced an increase in their income per capita from the 1970’s until nowa-days (table 3.1).

The analysis of Park and Mercado (2017) presents which are the main factors that have allowedcountries to move towards higher quintiles of the income per capita distribution, given their initiallevel. In addition, the authors try to answer whether the determinants of economic growth arethe same or vary over time. Their analysis is based on a sample of 182 countries from the year1964 to 2010’s. In order to find which factors enable countries to move to a higher quintile, theyconstruct probits with the potential determinants of growth as the independent variables. Theaccumulation of capital, both human and physical, as well as the discovery of oil resources are themain determinants in countries’ economic growth. However, the authors found that the relevanceof these factors vary not only over time but also depending on the income of countries. Indeed,there exist other factors like population growth, inflation or civil liberties that played an importantrole in certain periods of time.

McMillan et al. (2017) show which is the role played by the structural change and the sec-toral productivity growth on the aggregate labor productivity evolution of 7 developing countries(Botswana, Ghana, Nigeria, Zambia, India, Vietnam and Brazil). By decomposing the expressionfor aggregate labor productivity, they try to find how much of the changes in this variable can beattributed to the structural change and the within sectoral productivity evolution. Through thisanalysis it can be observed that there existed great differences in the structural changes of these7 developing countries.

In Costa et al. (2016a) and Costa et al. (2016b), the authors classify countries depending ontheir stage of development, given their income per capita growth rate and their position with re-spect to the economic leader. In order to show the factors that allow countries to grow and reachthe economic leader, the USA, the authors examine the evolution of Japan, China and Mexico. Theauthors claim that the development of countries is driven by a continuous growth in productivity,which is mainly due to the ability of countries to implement the advances in technology and man-agerial practices. In these analysis, authors find that institutions play an important role in thedevelopment of countries. Particularly, they observe that more opened institutions allow countriesto grow over larger periods of time.

Mamo et al. (2017) analyze how affected the mining sector to the development of countries.These authors use evidence from 3, 635 districts of 42 Sub-Saharan African countries for the period1992 − 2012. In this analysis, the development of a district is measured through the presence ofnight-time lights in it. The main finding in this article is that mining discoveries constitute an

1

Remaining Poor or Growing at a High Rate 2

opportunity for poor countries to develop. However, the only effects of a mining discovery on theincome per capita of a country are momentary since it is fulfilled the “resource curse” view.

The analysis of Duarte and Restuccia (2010) aims to answer if differences in the sectoralproductivity path among countries produce the observed differences in their structural changes.These authors elaborate a general equilibrium model in order to perform some replications indi-cating the relevance of each sectoral productivity growth. For this purpose, they construct a paneldata including 29 countries from 1956 to 2004. As a reference, the authors use the USA. This anal-ysis shows that structural transformation can initially increase aggregate productivity, but whencountries specialize in the services sector, their aggregate productivity decrease. In addition, theauthors claim that sectoral productivity differences among countries, in levels and growth, explainthe broad differences in their structural transformation and aggregate productivity paths.

In 2017, Ungor (2017) modified the general equilibrium model of Duarte and Restuccia (2010)disaggregating the industry sector in two sectors and the services sector in six sectors. This varia-tion in the model supposed an improvement in its estimations. Particularly, this analysis focuseson the role of sectoral productivity in the evolution of 11 Asian and Latin American countries from1963 to 2010. One finding of this analysis is that the stagnation of Latin American countries isdue to the poor growth of productivity in most sectors, rather than in a specific sector. The sec-ond finding of the analysis is that the manufacturing and wholesale sectors have a great positiveinfluence in the aggregate productivity evolution of countries.

Our analysis tries to see whether the differences in the sectoral productivity paths followedby the poorest countries can explain the differences observed in their aggregate productivity andincome per capita evolution. For this purpose, we use a model following the one elaborated byDuarte and Restuccia (2010) and the later modifications of Ungor (2017). In contrast to the orig-inal model of Duarte and Restuccia (2010), we consider that the economy can be decomposed in9 different sectors, like Ungor (2017). This will allow the model to capture better the labor real-location and the productivity growth of countries. Another important feature of our model thatdistinguishes it from the Ungor’s model is the implementation of the utility function similar to theone used originally by Duarte and Restuccia (2010). The utility function of Ungor (2017) assumesthat individuals consume only the amount of agricultural goods needed to survive, whereas theutility function of Duarte and Restuccia (2010) allows individuals to consume more agriculturalgoods than the necessary to survive. This model will enable us to obtain the aggregate productiv-ity and income per capita paths of countries, taking into account the performance in their sectoralproductivities and that countries may produce an amount of agricultural good higher than the re-quired to survive. Moreover, it will allow us to obtain the evolution of the aggregate productivityand income per capita of countries if they had experienced different sectoral productivity paths.Therefore, we will be able to evaluate the contribution of the productivity growth in each sector tothe evolution of the aggregate productivity and income per capita of countries. Given the interestin the lowest quintile and the lack of its sectoral information, our analysis is based on 9 countriesfor a period of 25 years, from 1975 to 2010.

The analysis will follow this structure:In the second section, we present the steps taken to perform our analysis and describe the data

that will be used for the initial analysis. In the following section are presented some observed factsregarding the evolution of the income per capita and aggregate productivity of the countries ana-lyzed. The fourth section contains the description of the model we use. The fifth section explainshow will be done the calibration of the model. The next section evaluates the performance of themodel by comparing its estimations with the data. After this, we present the results obtained


through the experiments. Finally, we review the main findings of our analysis and present severallines for further research.

Chapter 2

Description of data

The aim of this analysis is to study whether the paths in sectoral productivity experienced bysome of the poorest countries in 1975, determined their sectoral labor allocation and if so, what isits relevance in the aggregate productivity and on their income per capita. Particularly, we focuson the countries that were among the lowest quintile of the income per capita distribution in 1975and in 2010, in other words, that were among the 20% poorest countries at the beginning and atthe end of the period. Unfortunately, the analysis is restricted only to the cases for which there issectoral data available.

In the sample we use, although there are few observations, we can distinguish clearly differentpatterns in the income per capita evolution. Some of the countries in the sample were initiallyamong the poorest countries in terms of income per capita, but did a good performance and wereable to overcome poverty before 2010. Several countries that started also among the poorest,remained being poor. The remaining countries we analyze began the period in a higher quintile,but were not able to grow enough to maintain their position and became part of the poorest quintileby 2010. These differences let us analyze whether an specific allocation of resources has an impacton the aggregate productivity and the income per capita.

Firstly, we will get a general view, looking at the evolution of the GDP per capita and theaggregate productivity of countries, paying special attention to the countries in our sample. Inaddition, we present also the evolution of the sectoral productivity and labor allocation for thesecountries.

In this analysis, we will consider not only countries as individual cases, but we will gatherthem according to their income per capita evolution in three groups. This will enrich our analysisbecause it will allow us to see if countries with similar income per capita trends present somespecific characteristics that differentiate them from the other groups.

Secondly, we will present the model that will help us analyze whether changes in sectoralproductivity lead to sectoral labor reallocation affecting to the aggregate productivity of countries.We will calibrate the model using as a reference the US economy. Results from this model willbe presented and compared to what it is observed in the data. This comparison will be useful toevaluate the performance of the model in predicting the sectoral labor reallocation. The higherthe accuracy of the model, the more reliable would be the experiments done with it.

The analysis concludes analyzing what would have happened to the evolution of the relativeaggregate productivity with respect to the USA and the income per capita of some countries ifinstead of having their sectoral productivity had had the sectoral productivity of others. Par-ticularly, we would like to see how would have been the evolution of the sectoral allocation and

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the aggregate productivity of countries that remained or entered in the lowest quintile by 2010 ifthey had experienced the sectoral productivity of the countries that moved to a higher quintile.Moreover, it would be interesting to analyze what would have happened to the evolution of theaggregate productivity of countries that moved to a higher quintile if they had experienced somedifferent sectoral productivity evolution. These analysis can show the relevance of the sectoralproductivity in the aggregate productivity of countries.

2.1 Data

The data used in this analysis comes from two different data sets depending on the final purpose.If aggregate data is required, we use the Penn World Tables version 9.0 1(Feenstra et al., 2015),whereas if the analysis is done at the sectoral level, we rely on the sectoral information containedin the Groningen Growth and Development Centre (GGDC) 10-Sector database2(Timmer et al.,2015).

The Penn World Tables version 9.0 (from this moment PWT) gives information about aggre-gates of income, inputs and productivity of countries. We can find variables such as the realand current gross domestic product and the population engaged (labor) for 182 countries over theperiod 1950− 2014.

The income per capita of countries is the variable that we use to classify poor and rich coun-tries, and see how much they have improved, in economic terms, over the period studied. Theincome per capita of countries is measured as the Gross Domestic Product (GDP) per capita inPurchasing Power Parity terms (PPP). We obtain the GDP per capita in PPP terms dividing thereal GDP in PPP terms, from the PWT, by the population in each country from the same database.We consider the GDP in real terms to avoid possible biases produced by the inflation of countries.Using the income in PPP terms allows to compare the data from different countries because itestablishes a common set of international prices.

We will use this variable to analyze how was the income per capita distribution in 1975 andhow it has changed over the period studied. In addition, it will allow us to see which countries arein the extremes of the initial and final distributions, and how was the evolution of their incomeper capita over the period.

For the average annual growth rate of the income per capita, we will use the initial and finalincome per capita of countries calculated as the GDP of countries from the national accounts di-vided by their population (GDPpcna). Particularly, the average annual growth rate of the incomeper capita of country i, expressed as a percentage, has been computed as follows:((

GDPpcnai,2010

GDPpcnai,1975

) 12010−1975

− 1

)· 100.

Other important variable of the analysis is the productivity, in aggregate and in sectoral terms.We understand aggregate productivity as the production per worker of one country. Therefore,it is measured in terms of the real GDP in PPP of a country divided by the number of peopleengaged. Both variables are obtained from the PWT data set. There is an exception: in the caseof Botswana, from 1975 to 1979, there is no data on the people engaged. Since the average annualgrowth of the production per worker for 1980 − 2010 from the PWT and the GGDC databases are

1Available at http://www.rug.nl/ggdc/productivity/pwt/2Available at https://www.rug.nl/ggdc/productivity/10-sector/

http://www.rug.nl/ggdc/productivity/pwt/

https://www.rug.nl/ggdc/productivity/10-sector/


similar (1.039 with the PWT and 1.032 with the Groningen database), we will use the evolution ofthis variable observed with the Groningen database to estimate the aggregate productivity from1975− 1979 given its value for 1980.

The GGDC 10-Sector database considers 10 sectors in the economy: agriculture (AGR), mining(MIN), manufacturing (MAN), utilities (PU), construction (CON), trade services (WRT), transportservices (TRA), business services (FIRE), government services (GOV) and personal services (OTH).It provides information on the value added (current and constant in domestic prices) and theemployment in each of the previous activities for 42 countries. Since the data for Egypt considersjointly the government and the personal services (OTH2), as in Ungor (2017), we have gatheredthese sectors for all the countries and years. Therefore, the sectoral decomposition extends to atotal of 9 sectors. Another inconvenient is that the period of available information changes amongcountries. Although there are countries with available data from the 1950′s, there are others forwhich there is no data until the 1970′s. Therefore, we have considered the more restricted case toinclude the greatest amount of countries possible, which goes from 1975 until 2010.

In order to homogenize the analysis we will analyze the aggregate and the sectoral productivitydata for the period 1975− 2010.

The aim of this paper is to analyze only the performance of poor countries. Given the lack ofsectoral information, we study only 9 countries: Botswana (BWA), China (CHN), Egypt (EGY ),Ethiopia (ETH), India (IND), Kenya (KEN), Malawi (MWI), Senegal (SEN) and Tanzania(TZA). Almost half of them were poor in 1975, but could improve their income per capita notice-ably with respect to the other countries of the sample by 2010 (Botswana, China, Egypt and India).Two of them did not perform so successfully and remained being among the poorest countries in2010 (Ethiopia and Malawi). The remaining countries of the sample (Kenya, Senegal and Tanza-nia) were not in the lowest quintile of the income per capita distribution in 1975 but became by2010.

The sectoral productivity refers to the value added per worker generated by each sector. Giventhat the sectoral data is not measured in PPP terms, we cannot compare it directly between coun-tries. Therefore, we have converted it following Duarte and Restuccia (2010) and Ungor (2017)in order to have sectoral information that can be compared between countries. The idea of theseauthors is to calculate the constant value added in PPP terms generated by each sector dividedby the number of employees that produced it. The method they use so as to compute the sectoralproductivity is

V alue added sector iTotal value added ·GDP inPPP

Employmentii = a, 1, . . . , 8,

where the GDP in PPP terms comes from the PWT database and the remaining variables usedfor its computation from the Groningen data set. The inconvenient of this method is that it as-sumes that the relative prices across sectors remain constant. However, it has been found thatthe sectoral PPP-conversion differs over time (Duarte and Restuccia, 2010).

The sectoral labor allocation is a relevant characteristic of countries that affects their aggre-gate productivity and indicates their degree of development, given their stage in the structuraltransformation (Duarte and Restuccia, 2010). The sectoral labor allocation shows the percentageof the total labor force that is allocated to each sector.

Chapter 3

Observed facts

Table 3.1: Bounds and range of the quintiles1975 2010

Percent 20Min 279.99 556.56Max 1577.36 2563.13

Max/Min 5.63 4.61Percent 40

Min 1602.10 2629.2Max 2797.90 7423.71


Min 2890.86 7478.05Max 5980.52 15047.62


Min 6207.90 15419.46Max 12902.33 34770.87

Max/Min 2.08 2.25Ratio 80/20 8.18 13.57

Source: Own elaboration from the PWT

Each of the percentages on table 3.1 represents a quintile of the income per capita distribution.The 20 percent of the poorest countries, which are at the bottom of the income per capita distri-bution, represent the lowest or first quintile. The 40, 60 and 80 percentages represent the second,third and fourth quintiles respectively. We can observe that the income per capita has increasedfrom 1975 to 2010 in all the quintiles of the income per capita distribution.However, the behavior of the 80/20 ratio reflects that the income per capita has not grown thesame in all groups. This ratio indicates the difference in the income per capita of rich countriesin comparison to the income per capita of the poor ones. Its increase implies that the income percapita of the rich countries has grown much more than the income of the poor ones.

Table 3.1 shows that there are not only differences between distinct quintiles, but that the in-come per capita also varies within quintiles. This table presents the maximum and the minimum

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income per capita within each quintile. It is noticeable that there exists a greater difference be-tween the countries in the lowest quintile than between the countries in the highest quintile. Theevolution of this ratio shows that the difference between the maximum and minimum income percapita within a quintile has declined for the lowest quintile. On the contrary, this difference hasaugmented for the second quintile, whereas it has almost remained stable for the highest quintilesduring the 35 years analyzed.

Table 3.2: Poorest countries1975 2010

GDP per capita (in PPP) Country GDP per capita (in PPP) Country1 quintile 1 quintile

596.49 Ethiopia 1039.27 Ethiopia1219.81 Egypt 1043.87 Malawi1298.84 Malawi 2002.3 Tanzania1372.13 China 2122.80 Senegal1375.88 Botswana 2552.27 Kenya1400.81 India

2 quintile 2 quintile1650.49 Senegal 4386.10 India1894.83 Kenya1984.25 Tanzania

3 quintile9389.47 China9406.38 Egypt

12107.16 BotswanaSource: Own elaboration from PWT

As we have seen so far there is a great variety in the levels and the evolution of the incomeper capita of countries. This analysis focuses on the lowest quintile of the income per capitadistribution in order to study why some countries were able to grow faster and move to a higherquintile while others remained among the countries with lowest incomes. We focus our attentionin the lowest quintile because of the greater difference in income per capita between its members,the richest country has an income per capita 5 times higher the income of the poorest country.Given this notorious gap, it would be interesting to analyze the factors that allow some countriesat the bottom or in the middle of the lowest quintile to surpass the income per capita of the richestcountries in that quintile and move to a higher one, whereas other members of the lowest quintileremain in it. Table 3.2 contains the countries among this group in 1975 and 2010, for which thereare sectoral data available. Countries are colored depending on their income per capita evolution:they are blue if they were able to move to a higher quintile (group 1), red if they remained in thelowest quintile (group 2) and green if although starting in a higher percentile, they ended in thelowest one (group 3). By the side of each country is presented their income per capita.

If we make a deeper analysis, we can see that within the first quintile there were three levelsinitially: Ethiopia marked the lowest one, Egypt and Malawi were above it, but did not reachthe income of China, Botswana and India. Looking at the income per capita evolution of thesecountries, we can observe several facts that a priori could be unexpected, given their level ofinitial income per capita.


Egypt and Malawi had very similar income per capita in 1975, however, Egypt was able to growat a very high rate and end up in the third quintile by 2010, whereas Malawi remained to be verypoor. Can we explain these different patterns by their corresponding sectoral characteristics?What would have happened to Malawi if it had experienced the same changes as Egypt? Whatwould have happened to Malawi if it had experienced the same sectoral productivity paths as inEthiopia?Another interesting fact is the evolution of India with respect to the other members of the firstgroup. Why India, that was the country with the highest income per capita within the first quintilein 1975, ended the period in the second quintile while the other members of the first group finishedthe period in the third quintile?

The case of Tanzania is remarkable because although having the highest initial income percapita of the third group, it ended having the lowest income per capita of this group by 2010. Whatwas the difference between this country and the other members of the third group? In general,what was the difference between the third and the first groups?

Figure 3.1: GDP per capita evolution by groups

Source: Own elaboration from PWT

In figure 3.1, differences in the income per capita evolution among groups can be clearly appre-ciated. It is remarkable the increase in the income per capita experienced by countries of group1 from the late 1970’s. This growth allowed the first group surpassing the income per capita ofthe third group by the early 1980’s. Looking initial and the final years, we can observe that theincome per capita of groups 2 and 3 has increased slightly. However, there has not been a steadygrowth. Instead, the income per capita of groups 2 and 3 experienced a positive evolution until1985, followed by negative growth until 2005. After this year, economies in these groups seemed torecover, but between 2008 and 2009 they suffered a downturn from which they were able to recoverby 2010.

Table 3.3 indicates the average annual growth rates of the income per capita for each countryand group from 1975 to 2010. In this table we can see that only 3 of the 9 countries grew at arate lower than 1%, which is interpreted as the threshold to be considered in the Malthussiantrap (Costa et al., 2016a). Two of the countries inside the Malthussian trap were part of group


Table 3.3: Average annual growth rate of the income per capitaCountry Average annual growth (%)

BWA 4.88CHN 5.92EGY 4.03IND 3.81

Mean 4.66ETH 1.08MWI 0.53Mean 0.80KEN 0.68SEN 0.25TZA 1.15

Mean 0.70Source: Own elaboration from PWT

3 (Kenya and Senegal), while the other one was from the second group (Malawi). The remainingcountries of groups 2 and 3 grew at a rate slightly higher than 1%. Countries of group 1, however,experienced high annual growth rates ranging from almost 4% to 6%.

On average, we can observe that group 1 grew at a rate of about a 4.5 percent each year. Onthe contrary, groups 2 and 3 grew less than 1 percent each year.

Differences within groups are shown in figure 3.2. The income per capita evolution of thecountries in the first group is the most alike. China and Egypt grew around the mean, whereasBotswana and India were far from it. In the case of Botswana, the income per capita of the coun-try started being above the other members of the group by the early 1980’s. From that moment,the gap between Botswana and the other members of group 1 increased. On the contrary, Indiadifferentiates from its peers because its income per capita evolution was much slower. In fact, itis not until the second half of the 80’s decade, that a continuous positive growth is appreciated.Concerning the second group, it is remarkable that although the initial income per capita ofMalawi was much higher than the one of Ethiopia, their final incomes per capita are very simi-lar. Initially, we can observe a great difference in the level of income per capita of both countries.This gap seemed to reduce until the early 1980’s due to the increase in Ethiopia’s income, but itremained steady until the latest years, when the income per capita of Malawi decreased abruptlywhile the income per capita of Ethiopia kept growing. Nevertheless, their paths are full of sharpincreases and decreases of the income per capita.In group 3, there exists more diversity in the income per capita evolution. Initially, Tanzania wasthe country with the highest income per capita, but it experienced a significant decrease and itsincome per capita fell far below the income of Kenya and Senegal. This difference was accentu-ated until about 1995. From this year on, Tanzania increased its income per capita, and by 2010it came very close to the income per capita of Senegal. The income of Senegal did not experiencean stable behavior until 1980. That year, it started almost a decade of positive income per capitagrowth. However, it was followed by a fall in the income per capita of the country that lastedapproximately five years. From 1995, it is observed a continuous positive growth in the income percapita of Senegal. In the case of Kenya, the income per capita started below the one of Tanzania,but it had surpassed the latter by 1980. Even though the income per capita of this country did


Figure 3.2: GDP per capita evolution



not have a continuous evolution, we can observe that it grew until 1995. In this year, there wasa continuous fall that lasted almost a decade. From the early 2000’s, this country experienced anunprecedented continuous positive growth.

Table 3.4: Aggregate productivity1975 2010

BWA 5482.77 28691.94CHN 3045.85 16113.85EGY 4763.28 30675.86IND 4398.81 11075.12

Mean 4415.93 21639.19ETH 1483.74 2327.03MWI 3365.3 2713.35Mean 2424.52 2520.19KEN 5532.07 6816.35SEN 6408.97 6560.69TZA 4727.37 4643.38

Mean 5556.14 6006.81USA 61859.73 107893.8


Table 3.4 shows the production per worker or productivity for each country and group in 1975and 2010. Since the number of workers in a country is lower than its total population, figures ofaggregate productivity are higher than figures of GDP per capita. We can observe that countrieswith an initial GDP per capita lower than others, were above the latter in terms of aggregateproductivity. This is because of the differences on the labor force of countries. Therefore, coun-tries with lower income per capita and higher aggregate productivity have a lower percentage ofworking population than countries with higher income per capita and lower aggregate productiv-ity.1 We can observe that this is the case of Botswana with respect to India, Egypt with respect toMalawi and Kenya and Senegal with respect to Tanzania in 1975.

On average, we can see that the countries with the highest initial aggregate productivity arethe ones of the third group. However, there were countries of group 1, Botswana and Egypt, thatwere more productive than Tanzania. Group 1 was the second most productive, although Malawiwas able to surpass the Chinese productivity. In 2010, group 1 has the highest productivity. Thisgroup has, on average, a final aggregate productivity almost five times higher the initial one.Within this group, the most remarkable is the evolution of the aggregate productivity in Egypt.On average, groups 2 and 3 also raised their productivity, but at a much lower extent than group1. Within groups 2 and 3 we can find that Malawi and Tanzania have experienced a decreasedin their aggregate productivity. On the contrary, it is noticeable the increase of the aggregateproductivity in Ethiopia and Kenya.

1In order to clarify this idea, let us suppose a country i and a country j such that(GDP

Population

)i

<

(GDP

Population

)j(

GDP

Workers

)i

>

(GDP

Workers

)j

.


Looking at the aggregate productivity of the USA we can see that countries are still far fromit. However, its growth has been surpassed by the growth of the aggregate productivity of the firstgroup.

Figure 3.3: Aggregate productivity evolution by groups


Figure 3.3 shows the path followed by the aggregate productivity of each group. Similarly, towhat happened in the income per capita of groups, the first group surpassed the third one in the1980’s. Even though it is appreciated a positive trend in the growth of the aggregate productivityof group 1, this has not been as smooth as the evolution of its income per capita. The aggregateproductivity of group 3, initially the highest, has maintained around its initial level. The aggre-gate productivity of group 2, which initially was the lowest, has also remained around its initiallevel.

Given the similarity between the evolution of the income per capita and the aggregate pro-ductivity of countries observed from 1975 to 2010, we will try to analyze whether the behavior of

Alternatively, the GDP per worker can be expressed asGDP

Workers=

GDP

Population· PopulationWorkers

.

Therefore, it must be fulfilled that(GDP


)i

>

(GDP


)j

.

Since(

GDP

Population

)i

<

(GDP

Population

)j

, to fulfill the previous expresion we need(Population

Workers

)i

>

(Population

Workers

)j

.

This implies that(Workers

Population

)i

>

(Workers

Population

)j

.


the sectoral productivity of countries can explain the behavior of their aggregate productivity andincome per capita.

Figure 3.4: Aggregate productivity evolution within groups


Within groups countries also experienced differences in the paths of their aggregate produc-tivity. In the first group, the aggregate productivity Botswana was able to grow much faster thanthe other countries (figure 3.4). However, from 1995 this growth has experienced many ups anddowns. The growth of the aggregate productivity in Egypt was not so pronounced until the late1980’s, but from that year it has intensified and the aggregate productivity of this country alreadysurpassed the one of Botswana by 2010. The aggregate productivity of China did not start growingsignificantly until the late 1990’s, whereas the aggregate productivity of India did not start until2005. In group 2, the aggregate productivity of Malawi has maintained over the aggregate pro-ductivity of Ethiopia over the whole period analyzed, though the gap has decreased in comparisonto 1975. In group 3, it can be appreciated that there was a high gap of Kenya and Senegal withrespect to Tanzania until 1995. That year, the aggregate productivity of Tanzania started growingand the country was able to reduce the gap with the other members of group 3.

The evolution of the productivity does not only vary across countries, but is also different acrosssectors. Table 3.5 presents the average annual growth for the productivity in each sector for everycountry and group. On average, group 1 is the only group with positive growth rates in every


Table 3.5: Average annual growth rates of the sectoral productivityGroup 1 Group 2 Group 3

BWA CHN EGY IND Mean ETH MWI Mean KEN SEN TZA Mean USAAGR 2.37 1.97 5.39 1.09 2.71 7.28 1.70 4.49 0.87 -0.36 0.30 0.27 4.74MIN 8.65 6.11 6.30 2.75 5.95 -4.90 2.69 -1.11 -14.71 -1.43 0.57 -5.19 1.53MAN 1.37 5.19 5.39 3.25 3.80 -1.18 -1.34 -1.26 -2.12 -1.59 -2.38 -2.03 3.81PU 5.27 3.16 3.15 4.89 4.12 0.89 -0.03 0.43 0.53 7.70 -3.03 1.73 1.94

CON 4.45 0.71 5.37 -1.57 2.24 -3.51 -3.09 -3.30 -4.42 0.25 -1.50 -1.89 -0.97WRT 0.63 1.65 4.34 2.02 2.16 -0.82 -5.35 -3.09 -2 -2.83 -3.11 -2.65 2.51TRA 7.71 3.72 5.97 3.29 5.17 3.21 -1.77 0.72 0.08 0.18 -2.50 -0.75 3.16FIRE 3.54 5.51 4.12 1.28 3.61 1.31 -2.30 -0.50 1.78 0.09 -2.68 -0.27 0.81OTH2 -6.03 2.10 6.38 4.17 1.66 3.98 -3.98 0 -1.41 -0.36 -2.83 -1.53 0.40

Source: Own elaboration from GGDC 10-Sector Database

sector. In fact, group 1 has the highest growth rates in the productivity of all sectors, with the ex-ception of agriculture. Mining and transport services are the sectors in which this group has thehighest growth rates in productivity. Indeed, except India, the other three countries (Botswana,China and Egypt), have an impressive increase in the productivity in the mining sector. The sectorin which they had the lowest rate is personal and government services. This is due to the highdecrease of the productivity of Botswana in this sector. Within group 1, we can find that there is agreat difference between the productivity growth rates of India and those of the other countries ingroup 1. India experiences sectoral productivity growth rates much lower than the other countriesof its group for all sectors. This may explain why the aggregate productivity and the income percapita of India did not grow like the other members of group 1.Group 2 has the highest growth in agriculture. Countries of this group have especially decreasedtheir productivity in construction and trade services. It is remarkable the case of Malawi. Withthe exception of agriculture and mining, this country exhibits a decrease in the productivity of allsectors. Although Ethiopia had a negative evolution in the mining productivity, it achieved highgrowth rates in utilities and services sectors. Even though Malawi and Egypt had very similarincome per capita in 1975, we can see that they have followed very different paths in the sectoralproductivity. While Egypt experienced very high growth rates in the productivity of all sectors,Malawi decreased its initial productivity in almost all of them. This difference might explain whyEgypt moved to a higher quintile whereas Malawi remained in the lowest one.With respect to the third group, we can see that, on average, they have only experienced anincrease in the productivity of utilities or agriculture. They have especially decreased their pro-ductivity in the mining sector (due to the impressive fall in the productivity of the mining sectorin Kenya). In this third group, Tanzania is the country that exhibits a productivity fall in a highernumber of sectors (all but agriculture and mining). The negative evolution of the sectoral pro-ductivity in this group contrasts with the positive one experienced by the first group. Given thisdifference, it could be explained why the first group surpassed the third one in terms of aggregateproductivity and income per capita.In comparison to the growth rates of the sectoral productivity in USA, we can find that the rates ofgroups 2 and 3 are below them in all sectors. On the contrary, group 1 surpass the US productivitygrowth in mining, utilities, construction, transport and finance services.

An important feature that reflects the degree of development in countries is the share of labor


allocated to each activity. Usually, poor countries devote most of their resources to produce thebasic goods to survive. That is, most of labor is allocated to the agriculture sector. If they arewealthier they can devote part of this labor to manufacturing, reducing the share of labor inagriculture and increasing their productivity. When they become richer, they allocate part of thelabor force of manufacturing to the services sectors. Duarte and Restuccia (2010) found in theiranalysis that countries followed this pattern from 1956 to 2004. Moreover, the authors state thatthere was a general tendency, independent on the income of countries, that imply a reductionin the share of labor allocated to agriculture and an increase in the share of labor allocated toservices.

Table 3.6: Sectoral share of labor1975

Group 1 Group 2 Group 3BWA CHN EGY IND Mean ETH MWI Mean KEN SEN TZA Mean USA

AGR 1.02 1.16 0.69 1.13 0.67 1.03 0.97 0.88 1 0.9 1.11 0.8 0.03MIN 2.40 0.8 0 0.8 0.01 0 0 0 0 0 0 0 0.01MAN 0.23 1.14 1.60 1.03 0.09 0.67 1.33 0.03 0.82 1.64 0.55 0.04 0.2PU 0 0 4 0 0 0 0 0 0 0 0 0 0.01

CON 1.33 0.67 1.67 0.33 0.03 0 2 0.01 1 1 1 0.01 0.05WRT 0.63 0.42 1.89 1.05 0.05 1 1 0.03 0.8 1.6 0.6 0.05 0.22TRA 0.44 0.89 1.78 0.89 0.02 0 2 0.01 1.2 1.2 0.6 0.02 0.06FIRE 1.33 1.33 1.33 0 0.01 0 0 0 3 0 0 0 0.1OTH2 1.36 0.38 1.58 0.68 0.13 0.86 1.14 0.04 1.17 1.3 0.52 0.08 0.32

2010Group 1 Group 2 Group 3

BWA CHN EGY IND Mean ETH MWI Mean KEN SEN TZA Mean USAAGR 0.99 0.96 0.62 1.43 0.39 1.07 0.93 0.7 0.84 0.89 1.26 0.57 0.01MIN 2 2 0 0 0.01 0 0 0 1.5 0 1.5 0.01 0MAN 0.5 1.58 0.92 1 0.12 1.2 0.8 0.05 1.5 1.15 0.35 0.09 0.09PU 2 0 2 0 0.01 0 0 0 3 0 0 0 0

CON 0.4 1.07 1.6 0.93 0.08 0.57 1.43 0.04 1.13 1.5 0.38 0.03 0.05WRT 1.38 0.73 1.02 0.87 0.14 0.87 1.13 0.12 1.02 1.34 0.64 0.16 0.24TRA 0.57 0.76 1.71 0.95 0.05 0 2 0.01 1.13 1.13 0.75 0.03 0.04FIRE 1.74 0.77 0.99 0.5 0.04 0 0 0 1.5 0 1.5 0.01 0.18OTH2 1.17 1.06 1.39 0.39 0.18 0.71 1.29 0.07 1.24 0.88 0.88 0.11 0.37


Table 3.6 shows the average share of labor allocated by groups to each sector. The values forcountries represent how much greater or lower they are with respect to the mean of their group.The nearer the values of countries are to 1, the more alike the countries are within a group.2

As one might expect from their position in the income per capita distribution in 1975, thesecountries allocated most part of their labor force to agriculture, especially groups 2 and 3. Personaland government services was the second activity to which all groups allocated more labor. In group

2If the countries presented identical characteristics the mean would be the same value as the ones of the countries.Therefore, when dividing their values by the mean, we would obtain 1


1, manufacturing was the third activity that received a higher proportion of labor. Apparently, thisgroup of countries were more industrialized than the countries analyzed in the third group. In2010, all groups present lower shares of labor allocated to agriculture and larger shares allocatedto activities related to services in comparison to the beginning of the period studied, as Duarte andRestuccia (2010) found. It is remarkable the decrease in the share of labor allocated to agricultureby group 1 and the increase in the share of labor allocated to trade services by group 3.

Within group 1, it is noticeable that Egypt presented a distinct allocation of the labor forcefrom the other members of the group in 1975 (closer to a more developed economy). This countryallocated a much lower share of labor to agriculture and a higher proportion in manufacturingand all services, but finance services. Botswana also distinguished because of the higher shareof labor allocated to mining. Within group 2, there were also differences. Malawi allocated morelabor to manufacturing and services than Ethiopia. Nevertheless, both countries allocate a quitesimilar fraction of their labor force to agriculture. In group 3, it was remarkable the higher shareof labor allocated to mining and trade services by Senegal and to finance services by Kenya. Asfor group 2, all the three countries allocate a similar proportion of their labor force to agriculture.In 2010, Egypt still differentiates from the members of group 1 for the low share of labor allocatedto agriculture. This country also distinguishes from the others of its group for the higher sharesof labor allocated to some services (construction, transport, personal and government services).Apparently, the only country that do not show up the same transition to a more developed econ-omy is India, with a quite high labor share allocated to the agriculture sector, and a low laborshare allocated to services (lower than its group). It is noticeable the behavior of China, whichhas increased its share of labor allocated to mining until reaching the one of Botswana and hassurpassed the share of labor of its group in the manufacturing sector.In group 2, Ethiopia and Malawi ended up with quite similar labor shares in agriculture and man-ufacturing but not in services. Kenya differentiates in group 3 because of its higher shares of laborin most services sectors. Senegal distinguishes because of its low shares in mining and financeand its higher shares in construction and trade services. Tanzania differentiates for having highershares of labor in agriculture and lower shares in most services.

In table 3.7, are presented the sectoral shares of labor of the groups and the ones of the USA. In1975, we can see that the share of labor allocated to agriculture by the USA was much lower thanthe shares of the groups. However, the proportion of labor of this country allocated to manufactur-ing, trade, finance and personal and government services was much higher than the correspondingproportions of groups. In 2010, the initial pattern holds. It is appreciated that by 2010, all groupshave achieved a similar proportion of labor allocated to manufacturing than USA and in someservices.

Although there has been an increase in the industrial share of the labor force for the groupsthat equals it to the share of the USA, the agricultural shares are still high, which shows that thecountries of this sample have not completed the transition from the agricultural to the industrialsector. Group 1 is the group that has exhibited a higher transition of labor share from agricultureto manufacturing and services (mainly to trade services).

Figure 3.5 illustrates the evolution of the shares of labor allocated by groups to each sector. Inthe graphs we can see that the share of labor allocated to agriculture has decreased in all groups.It is appreciated that the share of labor in this sector was initially low in group 1 and its gap withthe other two groups has widened over the period analyzed. However, group 1 allocated a highershare of labor to the remaining activities, with the exception of trade services, in which group 3exhibit a higher increase. Graphs show that the activity that experienced the highest increase in


Table 3.7: Comparison of the sectoral shares of labor1975 Group 1 Group 2 Group 3 USAAGR 0.67 0.88 0.8 0.03MIN 0.01 0 0 0.01MAN 0.09 0.03 0.04 0.2PU 0 0 0 0.01

CON 0.03 0.01 0.01 0.05WRT 0.05 0.03 0.05 0.22TRA 0.02 0.01 0.02 0.06FIRE 0.01 0 0 0.1OTH2 0.13 0.04 0.08 0.32

2010 Group 1 Group 2 Group 3 USAAGR 0.39 0.7 0.57 0.01MIN 0.01 0 0.01 0MAN 0.12 0.05 0.09 0.09PU 0.01 0 0 0

CON 0.08 0.04 0.03 0.05WRT 0.14 0.12 0.16 0.24TRA 0.05 0.01 0.03 0.04FIRE 0.04 0 0.01 0.18OTH2 0.18 0.07 0.11 0.37



Figure 3.5: Sectoral share of labor by groups



the share of labor allocated to it was trade services.

Chapter 4

The model

In this analysis, we will use a general equilibrium model micro-funded that contains the mainideas of the model proposed by Duarte and Restuccia (2010) and later modifications done by Ungor(2017). Originally, the model was formed by the main 3 sectors (agriculture, industry and services),but Ungor (2017) disaggregated the industry sector into two sectors (mining and manufacturing)and the services sector into six sectors (utilities, construction, trade services, transport services,business services, government and personal services), since this can improve significantly theanalysis, as is shown in his article. Therefore, we will commit to the more detailed sectoral de-composition based on 9 different types of activities.

The model is static and its economy is only composed by households or families and firms,there is not a public sector nor an external one. Despite agents make their decisions consideringonly the present period, we can obtain the dynamics of variables, particularly the dynamics oflabor allocation. This is done by assuming that the sectoral productivity growth in the economy isexogenous.

On the one hand, households maximize their utility by deciding each period the amount ofconsumption of any of the nine type of goods. There are 9 different types of goods and servicesthat households can consume each period. Therefore, there are 9 sectors to which they mustprovide labor to produce what they consume. The only restrictions that households need to takeinto account are that their labor income must equal the value of their total consumption eachperiod and that they must consume above a certain level of the agriculture goods to survive. Sincethere is no capital, households cannot invest in any kind of assets.

On the other hand, firms look for maximizing their profits in perfect competition both, in thelabor and in the goods markets.

The economy reaches the equilibrium when all markets, those of goods and services and thoseof the production factors, clear.

4.1 Description

Firms and technology

The available sectoral technology affects not only the way firms produce goods and services, butalso to the amount they produce. In general, it is assumed that the higher the productivity level,the higher the amount of goods and services firms will be able to produce, holding the other fac-tors constant. Therefore, the production function of each sector represents the technological con-

21


straints faced by the firms. This model assumes that all the firms in each sector produce with thesame technology or production function, which depends on the specific technology of the activityand the share of total employment devoted to it. The following equation reflects the characteristicsof such production function for each sector

Yi = Ai · Li, for i = 1, . . . , 8, agriculture, (4.1)

where Yi is the production in sector i, Ai its specific technology and Li the share of total employ-ment in sector i.

The model assumes that firms maximize profits under perfect competition, both in the goodsand services and in the labor markets. Consequently and given that firms in each sector producewith the same technology, all firms face the same problem and consider the market prices forgoods, services and labor as given. The profits (π) maximization problem of a representative firmof sector for i = 1, . . . , 8 and agriculture, can be expressed as

maxLi{πi = pi ·Ai · Li − ω · Li} ,

where pi represents the market price for the good or service produced by sector i, ω are the wagesreceived by employees as a payment for their work and Li is the amount of labor in sector i. Sinceall firms in each sector behave the same, the decision problem of one of its firms may reflect thebehaviour of the whole sector.

Households and preferences

In this model, families or households have an infinite period life. We will normalize the size ofhouseholds to 1 each period. Every period they try to maximize their utility choosing the amountof goods and services they want to consume. For this purpose, they must take into account thebudget constraint, that is, they must consider that their expenditure has to be equal to the incomethey obtain for providing labor to the firms. Households offer labor to firms inelastically, in otherwords, they spend all the time they have working because leisure does not give them utility. Animportant distinctive feature of this model is that it assumes that preferences are non-homotheticwhen introducing a minimum consumption of agricultural goods needed to survive. Since the onlyproduction factor is labor, there is no physical nor human capital, households do not have thepossibility to invest in these kind of assets.Preferences of a representative household can be expressed as

∞∑t=0

βt · u (ct, ca,t) , β ∈ (0, 1)

where β represents the discount factor and u (ct, a) is the utility of households for each period.The discount factor is the relative value attached by households to future levels of consumptionand utility in order to express their value in the present. Therefore, greater values of β indicatethat households value more the future. The utility depends on the consumption of the agriculturalgood ca,t and the combination of consumption of the other goods and services ct as follows:

u (ct, ca,t) = a · ln (ct) + (1− a) · ln (ca,t − a) .

The parameter a indicates what is the relative preference of non-agricultural goods relative to theagricultural ones. The parameter a refers to the minimum level of consumption in agriculture


needed to survive. The variable ca,t reflects the agricultural consumption while ct is a combinationof the non-agricultural goods and services. This latter combination has the following structure

ct =

(γ

1η

1 · cη−1η

1,t + . . .+ γ1η

8 · cη−1η

8,t

) ηη−1

.

The problem that households solve every period in order to maximize their utility is

max{ct,ca,t}

{a · ln

(γ

1η

1 · cη−1η

1,t + . . .+ γ1η

8 · cη−1η

8,t

) ηη−1

+ (1− a) · ln(ca,t − a)

}subject to pa · ca,t + p1 · c1,t + . . .+ p8 · c8,t = ω

where η is the elasticity of substitution between non-agricultural goods or services and γi is theweight that the household gives to the consumption of good or service i. Therefore, the sum of γimust be equal to one. The budget constraint restriction impose that households cannot save norhave debts, they must consume each period all the labor income they obtain.

Market clearing

The markets in the economy “clear” when their offer and demand coincide. The conditions thatmust be fulfilled to ensure that markets clear are:

In the labor market

This market will clear if all the labor offered by households equal the labor hired by firms. There-fore, if the firms of every sector i demand a proportion, Li, of the labor offered by households,the sum of all these proportions must equal 1, which represents the 100% of the labor offered byhouseholds.

La + L1 + L2 + · · ·+ L8 = 1 (4.2)

In the goods and services market

When the demand of goods and services done by households coincide with the quantity of goodsand services produced by firms these markets clear. The following equations reflect those condi-tions

ca = Ya, c1 = Y1, c2 = Y2, . . . , c8 = Y8. (4.3)

Competitive equilibrium

Given a set of market prices for the goods and services {pa, p1, p2, · · · , p8} and the wage rate perunit of work {ω} of the economy, the economy will be in equilibrium if the decisions taken byhouseholds when maximizing their utility {ca, c1, c2, · · · , c8} and the ones taken by firms whenmaximizing profits, {La, L1, L2, · · · , L8}, are such that all markets clear

La + L1 + L2 + · · ·+ L8 = 1 andca = Ya, c1 = Y1, c2 = Y2, . . . , c8 = Y8.


Model solution

Firms

The solution for the decision problem of the firms is given by its first order condition, which canbe obtained by computing the first derivative of the profits with respect to the labor and equatingit to 0.

∂πi∂Li

= pi ·Ai − ω = 0 =⇒ pi ·Ai = ω.

The condition obtained from it shows that firms hire labor until the value of its marginal produc-tivity equals its marginal cost. In other words, firms hire labor until the profit they obtain withthe last unit of labor hired pi · Ai is equal to the cost that generates this last unit of labor to thefirm ω. Otherwise, if the revenue they obtained by hiring one more unit of labor is higher (lower)than the cost, the firms would hire one more (less) unit of labor.If we normalize wages to 1, we can obtain from the first order conditions of firms that the price ofgoods and services depend inversely on their productivity. In order to fulfill the first order condi-tion and holding wages constant, this implies that the greater (lower) is the available technologyin a sector, the lower will be the price (greater) of the good or service produced.

pi =1

Ai, for i = 1, . . . , 8, agriculture. (4.4)

Households

Initially, we will study how households distribute their non-agricultural consumption among theother goods and services available. Having the optimal combination of consumption for non-agricultural goods and services, we will use it to obtain the optimal agricultural consumption.

Solving for the consumption of non-agricultural goods Firstly, we will analyze how house-holds distribute their consumption among the non-agricultural goods or services such that the costof the whole non-agricultural consumption is minimized. For this purpose, households minimizethe non-agricultural consumption cost given the structure of the non-agricultural consumption.Alternatively, this decision problem can be solved by maximizing the non-agricultural consump-tion taking into account the budget constraint.

Therefore, we need to solve the following constrained maximization problem:

max{ci}i≥0

ci =

(γ

1η

1 · cη−1η

1 + . . .+ γ1η

8 · cη−1η

8

) ηη−1

subject to pa · ca +8∑i=1

pi · ci = ω

for i = 1, . . . , 8.Normalizing wages to 1, it would be expressed as

max{ci}i≥0

ci =

(γ

1η

1 · cη−1η

1 + . . .+ γ1η

8 · cη−1η

8

) ηη−1


pi · ci = 1


To solve this problem we will use the Lagrange multiplier

L =

(8∑i=1

γ1η

i · cη−1η

i

) ηη−1

+ λ ·

(1− pa · ca −

8∑i=1

pi · ci

).

and differentiate it with respect to the different types of non-agricultural consumption

∂L∂ci

=η

η − 1·

(8∑i=1

γ1η

i · cη−1η

i

) ηη−1−1

· γ1η

i · cη−1η−1

i · η − 1

η− λ · pi = 0, ∀i = 1, . . . , 8

Through simple algebraic manipulation (see Appendix A), we obtain the following expression forthe non-agricultural relative consumption.

cjci

=

(pipj

)η· γjγi

(4.5)

Rearranging terms of the first order conditions we can see that household will decide howmuch to consume of each good or service depending not only on its preferences γj

γi, but also on its

relative price pipj

. The greater are the preferences for one good or service, the higher will be theconsumption of that good or service. As one might expect also, the greater the price of a good orservice with respect to the price of another, the lower will be the consumption of the first withrespect to the consumption of the second good or service.

By considering the clearing condition for the labor market (equation 4.2), the production func-tion (equation 4.1), the clearing condition for the goods market (equation 4.3), the equation forthe relative non-agricultural consumption (equation 4.5) and the equation from the firm’s decisionproblem (equation 4.4) we get the following expression for the non-agricultural shares of employ-ment (see Appendix A).

Li =γiA

η−1i (1− La)8∑i=1γiA

η−1i

, (4.6)

which can be expressed as

Li =1− La

1 +8∑

j=1, j 6=i

(AiAj

)1−η γjγi

.

This alternative way of expressing the sectoral labor allocation shows that our expressions areconsistent with those of Duarte and Restuccia (2010). Implementing the clearing condition forthe goods and services market (equation 4.3) and the production function (equation 4.1), we canobtain an expression for the total consumption of non-agricultural goods and services in terms of


the sectoral employment.

C =

(8∑i=1

γ1η

i · cη−1η

i

) ηη−1

=⇒

Implementing the clearing conditions for the goods and services markets

C =

(8∑i=1

γ1η

i · Yη−1η

i

) ηη−1

=⇒

Implementing the production function

C =

(8∑i=1

γ1η

i · (Ai · Li)η−1η

) ηη−1

.

Substituting the expressions for the sectoral employment obtained previously (equation 4.6) wecan express the total consumption of non-agricultural goods in terms of the labor force in theagriculture sector, which will help us to determine the consumption of agricultural goods (seeAppendix A).

C =

8∑i=1

γiAη−1i(

8∑i=1

γiAη−1i

) η−1η

(1− La)η−1η

ηη−1

Applying logarithms,

lnC =

η

η − 1ln

7∑i=1γiA

η−1i(

8∑i=1γiA

η−1i

) η−1η

+ ln (1− La)

. (4.7)

Solving for the consumption of agricultural good Secondly, we can solve for the optimaldecision between the combination of all non-agricultural goods and the consumption of the agri-cultural good, taking into account that we have obtained, in the first step, the optimal expenditureamong all non-agricultural goods for a given combination of all non-agricultural goods. For thispurpose, we will substitute the expression for the logarithm of the combination of non-agriculturalconsumption (equation 4.7) in the household’s decision problem1 (see Appendix A).

maxLa≥0

U = maxLa≥0

(1− a) · ln (ca − a) + a · ln[γ

1η

1 · cη−1η

1 + . . .+ γ1η

8 · cη−1η

8

] ηη−1

=⇒

maxLa≥0

U = maxLa≥0

(1− a) · ln (AaLa − a) + a ·η

η − 1ln

7∑i=1

γiAη−1i(

8∑i=1

γiAη−1i

) η−1η

+ ln (1− La) .

1Given that this model assumes that there are no distorsions, the solution obtained from the equilibrium and theoptimal solution coincide. Therefore, the equilibrium conditions can be introduced in the household’s decision problem.


Now, we can solve for the optimal decision by differentiating with respect to the labor in agricul-ture, we can obtain an expression for it.

∂U

∂La=

(1− a) ·AaAa · La − a

− a · 1

1− La= 0 =⇒

(1− a) ·AaAa · La − a

= a · 1

1− La=⇒

(1− La) · (1− a) ·Aa = a · (Aa · La − a) =⇒

(1− a) = a · La + (1− a) · La −a · aAa

=⇒

La = (1− a) +a · aAa

. (4.8)

The expressions for the sectoral employment obtained in this section are similar to the ones ofDuarte and Restuccia (2010) and Ungor (2017). In the Appendix B, we check if the labor marketclears by introducing the expressions obtained for the sectoral employment.

4.2 Calibration

The parameters of the model can be classify in two main groups. On the one hand, we can findthe values of the parameters that determine households’ preferences (a, γ and η). On the otherhand, we can find the values of the technological parameters, particularly those reflecting theinitial sectoral productivity (Ai). Following Duarte and Restuccia (2010) and Ungor (2017), wewill obtain these parameters using as a reference the USA data for 1975.

Once we have calibrated these parameters, they will allow us to simulate the productivity,income per capita and sectoral labor allocation paths of the countries for the period 1975− 2010.

Calibration of the preferences parameters

The parameters that determine the preferences of households are considered to be the same acrosscountries and constant over time. Otherwise, it would be difficult to determine how much of thechanges in the sectoral labor allocation were caused by fluctuations in the sectoral productivity orin the preferences.

Calibration of a

The parameter that weights the utility between agricultural and non-agricultural consumption,1− a, will be calibrated to mimic the share of labor allocated to agriculture in the USA in the longrun. Following Duarte and Restuccia (2010), 1 − a will be equal to 0.01. Consequently, a will be0.99.

Calibration of γ

With the aim of simplifying the analysis, we will normalize the initial productivity across sectorsfor the USA, setting their initial parameters equal to 1, Ai,1975 = 1 for i = a, 1, . . . , 8. Given thisnormalization, we will consider the equation for the non-agricultural shares of labor (equation4.6) to obtain an expression for the weights of the utility among the non-agricultural goods and


services consumption, γi. Considering that these weights add up to 1, these equations show that γican be calibrated as the share of labor allocated to the corresponding sector i without consideringthe agriculture observed for the USA in 1975 .

Li =γiA


η−1i

=⇒

Li =γi · (1− La)∑

i=1,...,8 γi=⇒

Li = γi · (1− La) =⇒

γi =Li

1− La∀i ∈ [1, 8]

Table 4.1 presents the values of these parameters.

Table 4.1: Calibration of parametersParameter γ1 γ2 γ3 γ4 γ5 γ6 γ7 γ8

Value 0.0086 0.2045 0.0069 0.0538 0.2291 0.0593 0.1057 0.3322

Calibration of a

Introducing the value calibrated for a in the equation of labor in agriculture (equation 4.8), we canobtain the value of the parameter a as follows

a =La − (1− a)

a=⇒

a =(2871.24/92032.1)− 0.01 (1 + 0)

0.99=⇒

a = 0.0214.

Calibration of η

To estimate the value for η we will impose that the estimated average annual growth for the USaggregate productivity is equal to the observed one. To calculate the average annual growth ofaggrergate productivity, we will introduce the previous parameters and the required data for theUSA in 1975 in the expressions for the aggregate productivity. The condition considered to obtainthe value of η is (

A2010 (η)

A1975 (η)

) 135

− 1 = 1.016 =⇒(A2010 (η)

A1975 (η)

) 135

− 0.016 = 0,

where the aggregate productivity of year t is given by the sectoral productivity of the USA inperiod t, t = 1975, 2010, and the sectoral shares of labor estimated for the period t as functions of


η, given this data.At (η) =

∑i=a,1,...,8

Ai,t · Li,t (η)

The sectoral shares of labor in terms of η are given by the expressions of the sectoral employmentobtained in the model.2

La,t = (1− a) +a · aAa,t

Li,t =γiA

η−1i,t (1− La,t)8∑i=1γiA

η−1i,t

i = 1, . . . , 8

Following the process described, we obtain that η is equal to 0.2301.

Calibration of the initial sectoral productivity

Having calibrated the values for the preferences parameters of the model and considering theinitial sectoral shares of labor and aggregate productivity observed for each country, we can obtainthe values of the initial sectoral productivity for each country through the following system ofequations

Li,1975 =γiA

η−1i,1975 (1− La,1975)

8∑i=1γiA

η−1i,1975

i = 1, . . . , 8

La,1975 = (1− a) +a · aAa,1975

A1975 =∑

i=a,1,...,8

Ai,1975 · Li,1975

where i refers to the sectors i. Given the lack of information on the people engaged (number ofworkers) for Botswana from 1975 to 1979, we will measure the aggregate productivity of this coun-try with the GGDC 10-Sector database as the total value added divided by the total employment.

Following Duarte and Restuccia (2010) and Ungor (2017), aggregate productivity will be mea-sured in relative terms to the USA. As a consequence, the resulting sectoral productivity will bemeasured in terms of the US productivity. Measuring these variables in relative terms to theUSA will allow us to minimize the inconvenient caused by the lack of sectoral information in PPPterms.

Table 4.2 shows our estimations for the initial level of labor productivity in relative terms tothe USA. According to these estimations, countries had already a great productivity in finance,whereas it was very low in agriculture. With the exception of Botswana, our estimations reflectthat countries of group 2 had higher sectoral productivity than countries of group 1. Countries ofgroup 3 had the highest productivity, although Botswana surpassed them in some activities.

2In this case, the initial sectoral productivity will not be normalized, it will take its corresponding value. However, itwould be similar to normalize it and use the corresponding final value. This is because the ratio between them is used.Since in both cases, the growth rate is the same, the ratio between the final and the initial value would be the same.


Table 4.2: Estimated sectoral productivity levels in 1975AGR MIN MAN PU CON TRA WRT FIRE OTH2

BWA 0.0318 0.0311 4.4799 0.3173 0.2939 2.9204 1.3027 4.1324 0.4007CHN 0.0278 0.0084 0.0395 0.0875 0.0768 0.2990 0.0891 0.5827 0.2077EGY 0.0470 0.2476 0.0705 0.0406 0.0474 0.1509 0.0781 0.9487 0.0802IND 0.0236 0.1383 0.0289 0.0316 0.0533 0.0145 0.0404 0.4487 0.0231ETH 0.0296 0.0714 0.0909 0.0959 0.2286 0.2242 0.0969 2.1054 0.1843MWI 0.0269 0.2233 0.4198 0.2442 0.4840 0.3424 0.2051 1.1812 0.2384KEN 0.0252 0.2167 0.1490 0.0814 0.0556 0.2362 0.1263 2.0248 0.2871SEN 0.0299 0.4005 0.2623 0.0972 0.3471 0.1944 0.1734 9.0918 0.2459TZA 0.0240 0.1261 0.7088 0.3710 0.3349 0.3293 0.3211 3.9125 0.4762

Computation of the sectoral productivity path

The initial values of the sectoral productivity will allow us to to obtain the whole path of thesectoral productivity. We can obtain the value for the sectoral productivity of next years by mul-tiplying the initial values with the growth in the corresponding sectoral productivity. In order toobtain the growth rate in the corresponding sectoral productivity, we calculate the sectoral pro-ductivity as the corresponding sectoral value added (V A) divided by the employment of that sector(EMP ). 3 The sectoral productivity growth rate for a period t, is calculated as

V Ai,tEMPi,tV Ai,t−1

EMPi,t−1

− 1 t = 1976, . . . , 2010.

Table 4.3 shows the average of the annual growth rates of the sectoral productivity for each

Table 4.3: Average annual growth of sectoral productivity(%)AGR MIN MAN PU CON TRA WRT FIRE OTH2

BWA 2.96 6.69 9.57 5.29 5.24 2.83 6.98 5.81 3.24CHN 1.75 7.03 6.12 4.87 1.72 2.16 3.56 5.25 2.34EGY 2.89 6.33 3.00 3.66 3.33 2.17 4.16 2.87 3.80IND 1.47 3.32 3.52 4.73 0.18 2.35 3.19 1.11 4.62ETH 0.01 -5.33 -0.87 -0.07 -3.04 -1.93 1.90 3.40 1.65MWI 1.42 5.82 0.26 2.68 -0.56 -2.96 0.42 1.57 -1.28KEN 0.16 -1.82 -1.38 0.61 -3.57 -1.67 -0.14 1.60 -1.75SEN -0.25 -1.52 -2.21 6.04 -0.44 -3.70 -0.81 0.45 -1.17TZA 1.07 -1.74 -0.59 0.01 -2.28 -3.07 -0.25 -0.18 0.71USA 4.38 1.30 3.04 2.36 -1.77 1.86 2.71 0.44 -0.08

country. The figures in this Table differ from those in Table 3.5 because the sectoral productivitiesin this Table are not PPP adjusted. Nevertheless, again, it is noticeable that the only countriesthat experienced a positive growth in all the sectors are the ones of group 1.

3In contrast to the sectoral productivity of the initial analysis, in this case the sectoral productivity is not adjustedin PPP terms. If we obtained the growth rate from the data measured in PPP, it would not only reflect the changes inthe sectoral production but it also would show the changes in the international relative prices.


4.3 Simulation

Given the values we have obtained for the parameters and the observed data, we can simulate theevolution of the sectoral shares employment, the relative aggregate productivity and income percapita of countries from 1975 to 2010. By comparing these series with the real data, we will getthe accuracy of the model. Later on, comparing these simulated series with their correspondingpaths when changing the sectoral productivity, we will observe the relevance of each sector in theevolution of countries.

4.3.1 Simulation of the sectoral shares of employment

Having calculated the sectoral productivity for all years, we can obtain the simulated series forthe sectoral shares of employment for 1975− 2010 by substituting the corresponding values in theexpressions for the sectoral shares of labor obtained in the model

La,t = (1− a) +a · aAa,t

t = 1976, . . . , 2010

Li,t =γiA

η−1i,t (1− La,t)8∑i=1γiA

η−1i,t

i = 1, . . . , 8; t = 1976, . . . , 2010.

By comparing the resultant shares of labor with the observed ones, we will have an idea on theperformance of the model. This is, whether the model gives or not simulations close to the data.

4.3.2 Simulation of the relative aggregate productivity and the income percapita of countries

Once we have the exogenous series for the sectoral productivity and the simulated series for theshares of labor, we can obtain the relative aggregate productivity of countries. The followingexpression gives the relative aggregate productivity for the country j and the period t

Yj,t = Aaj,t·Laj,t +A1j,t·L1j,t + · · ·+A8j,t·L8j,t. (4.9)

The relative aggregate productivity of countries can be easily obtained by plugging the correspond-ing simulations for the sectoral shares of labor (L) and the computed sectoral productivity into theexpression 4.9. Therefore, a sectoral productivity path will imply a specific evolution of the aggre-gate productivity of a country. By comparing the changes in the relative aggregate productivityresultant from different sectoral productivity paths, we can identify the sector responsible for thegood performance of countries. In addition, we can observe what have been the sectors leading theevolution of the relative aggregate productivity of countries.

The income per capita of countries can be estimated as follows

GDPpcj,t = Yj,t·yUSA,t·Lj,tPopj,t


4where GDPpcj,t refers to the income per capita of country j in period t, Yj,t is the relative aggre-gate productivity of country j in period t, yUSA,t is the aggregate productivity of the USA in theyear t, Lj,t are the workers of country j in period t and Pop is the population of country j in periodt.

Changes in the income per capita of countries also allow us to see which sectors are responsiblefor their good performance, in terms of income per capita.

4.4 Evaluation of the model

The results obtained through the model can be close or really far from what has really happened.Following Duarte and Restuccia (2010) and Ungor (2017), we will evaluate the model in two dif-ferent ways.

To know if model is able to replicate what has happened in the countries, firstly, we will lookat the figures 4.1 and 4.2. The better performs the model, the more alike will be the data andthe simulations. If the simulation and the data coincide, the country will be represented on the45-degree line of the graphs. If countries are above that line, it indicates that the simulations ofthe variable are lower than the corresponding values observed in the data. On the contrary, ifcountries are below the line, the simulations are higher than the data.

In figure 4.1 is presented the similarity between the data and the simulations of the sectoralshares of labor for 2010. In general, the simulations are not very accurate. However, the modelgives very precise simulations for the sectors of utilities, mining, except for China, for financeexcept BWA and USA, and it gives quite good simulations for personal and government services.The model also performs very accurately in specific cases like the USA in agriculture, Botswanain manufacturing and China, Malawi, Tanzania, Ethiopia and Senegal in the finance sector. Inaddition, this figure contains a comparison between the data and the simulations of the finalaggregate productivity. In this case, the model is able to replicate the data better than in mostsectors.

Figure 4.2 shows how is the percentage change observed in the sectoral shares of labor from1975 to 2010 and what is the predicted percentage change in each case. In general, we can seethat the simulated changes in labor allocation are not the same as the observed ones, but in somecases are quite close. In mining, simulations are very alike to data for almost all countries butEthiopia. In construction, simulations are good except for Ethiopia and Senegal. In general,simulations for personal and government services are quite close to the observed data. However,the simulations for the changes in the sectoral shares of labor replicate better the data than thesimulations for their levels in 2010. Paying attention to the performance of the model by countries,

4Given the expressions for the income per capita and the aggregate productivity we have that

GDPpci,t = Yi,t·yUSA,t·Li,tPopi,t

GDPpci,t =

GDPi,tLi,t

GDPUSA,tLUSA,t

·GDPUSA,tLUSA,t

· Li,tPopi,t

GDPpci,t =GDPi,tLi,t

· Li,tPopi,t

GDPpci,t =GDPi,tPopi,t

.


Figure 4.1: Comparison between the simulated and the observed sectoral shares of labor


Figure 4.2: Comparison between the simulated and the observed changes in sectoral shares oflabor


we can find that it performs very accurately for the USA. Though at a lower extent than the USA,the model also gives very accurate simulations for India and Malawi. On the contrary, simulationsfor Ethiopia are very distinct from data. This figure, contains also a comparison of the observedand simulated change in the aggregate productivity relative to the USA. In this aspect, the modelperforms better in simulating the levels for 2010 than the changes of this variable over the periodanalyzed.

Secondly, we present several statistics in table 4.4 that show more formally the performanceof the model.

In the first row of each country is presented the sectoral Root Mean Square Error (RMSE)statistic. The RMSE is computed as √∑T

t=1 (zt − zt)2

T,

where T is the number of years in the period considered, zt is the observed sectoral share of laborin period t and zt is the simulated sectoral share of labor for the same period. Since the differencebetween the observed and the simulated value is elevated to the second power, the statistic willalways be positive. When the difference between the data and the simulation from the model islarge, the statistic takes values far from 0. Therefore, when the statistic is close to 0, the differencebetween the data and the model is lower, this is, the simulations of the model are more accurate.

In table 4.4, we can find that, in general, the values for this statistic are low. Mining andutilities sectors are the activities that present the best results, while agriculture and personal andgovernment services are the sectors with higher figures. With respect to the relative aggregateproductivity, this statistic takes low values. In general, this statistic shows that the countries forwhich the model gives more accurate simulations are the USA and India.

The second row of each country contains the sectoral Modified Nash-Sutcliffe Efficiency crite-rion (mNSE). This statistic derivates from the Nash-Sutcliffe efficiency criterion (NSE), which iscalculated as

1−∑T

t=1 (zt − zt)2∑Tt=1 (zt − µz)2

.

It measures the distance between the data and the simulations with respect to the distance be-tween the data and the mean. When simulations and data coincide, the statistic takes value 1.The greater is the distance between the simulation and the data, the lower is the value. However,this statistic is affected by the scale of the data. Given the consideration of values to the secondpower, differences in data with high values can be overestimated, while differences in data withlow values can be considered 0. The mNSE criterion avoids this inconvenient by considering thedifferences in absolute value instead of using the square.

mNSE = 1−∑T

t=1 (|zt − zt|)∑Tt=1 (|zt − µz|)

We can see that the values that this statistic takes with the data analyzed are far from 1. It isremarkable the figures of this statistic for India, country for which the statistic takes positivevalues in most sectors. In general, this statistic indicates that simulations for the sectoral sharesof labor and relative aggregate productivity are not very good.


Table 4.4: Statistics to evaluate the performance of the modelAGR MIN MAN PU CON TRA WRT FIRE OTH2 Rel. Aggr.

Productivity

Botswana

RMSE 0.32 0.02 0.02 0.01 0.03 0.06 0.02 0.03 0.16 0.13

mNSE -2.01 -2.79 -0.06 -1.04 0.20 -0.05 -1.46 -0.92 -8.88 -0.93

md 0.25 0.22 0.51 0.33 0.65 0.50 0.28 0.33 0.09 0.33

CORR 0.21 0.19 0.71 0.23 0.71 0.68 -0.09 0.17 -0.61 0.26

China

RMSE 0.12 0.01 0.03 0 0.03 0.03 0.01 0 0.02 0.05

mNSE -0.18 -2.76 -1.25 -0.45 -0.44 -0.03 -0.24 0.24 0.50 -1.11

md 0.59 0.19 0.44 0.53 0.55 0.65 0.59 0.70 0.78 0.32

CORR 0.99 0.18 0.88 0.93 0.98 0.98 0.96 0.87 0.99 0.68

Egypt

RMSE 0.06 0 0.06 0 0.02 0.04 0.02 0.01 0.01 0.06

mNSE 0.09 -0.33 -9.73 -1.17 -0.34 -0.88 -1.74 -0.20 0.44 0.06

md 0.66 0.27 0.08 0.40 0.40 0.40 0.27 0.06 0.65 0.57

CORR 0.98 0.03 -0.48 0.91 0.72 0.91 0.52 0.71 0.80 0.97

Ethiopia

RMSE 0.42 0 0.09 0 0.02 0.17 0.01 0 0.12 0.03

mNSE -10.34 -2.15 -5.64 -16.33 -3.33 -10.36 -30.22 -3.49 -23.72 -3.71

md 0.08 0.24 0.13 0.05 0.19 0.08 0.03 0.45 0.04 0.27

CORR -0.06 -0.46 -0.16 -0.41 -0.09 0.05 0.26 0.04 -0.47 0.70

India

RMSE 0.06 0 0.02 0 0 0.01 0.01 0.01 0.02 0.03

mNSE 0.20 -1.01 -1.10 -2.50 0.88 0.60 0.29 0.39 -2.73 -1.85

md 0.71 0.41 0.48 0.14 0.94 0.82 0.68 0.18 0.09 0.26

CORR 0.96 0.47 0.91 -0.46 0.99 0.97 0.94 0.97 -0.43 0.78

Kenya

RMSE 0.20 0 0.05 0 0 0.06 0.01 0.01 0.05 0.05

mNSE -0.69 0.31 -0.42 -1.67 0.36 -0.62 -0.58 -1.61 -1.58 -1.17

md 0.37 0.62 0.41 0.27 0.67 0.38 0.39 0.64 0.28 0.44

CORR 0.54 0.92 0.79 0.14 0.86 0.65 0.49 -0.61 0.17 0.88

Malawi

RMSE 0.18 0 0.04 0 0.02 0.05 0.01 0.01 0.05 0.04

mNSE -2.43 -1.88 -5.50 -4.53 -2.27 -0.80 -2.10 -1.18 -2.27 -2.90

md 0.35 0.08 0.15 0.09 0.35 0.50 0.36 0.38 0.34 0.20

CORR 0.70 -0.44 0.25 -0.18 0.71 0.78 0.61 0.45 0.69 0.56

Senegal

RMSE 0.54 0 0.10 0.01 0.03 0.22 0.03 0 0.15 0.06

mNSE -7.18 -4.18 -5.78 -1.52 -2.24 -4.20 -6.15 -2.76 -37.83 -2.48

md 0.10 0.20 0.13 0.29 0.23 0.16 0.11 0.20 0.02 0.31

CORR -0.40 0.44 -0.25 -0.30 -0.27 -0.52 -0.03 -0.36 0.17 0.77

Tanzania

RMSE 0.09 0 0.02 0 0.01 0.03 0.01 0 0.03 0.04

mNSE -1.06 -0.70 -2.25 0.66 -1.44 -1.01 -1.74 -0.10 -0.85 -1.42

md 0.46 0.34 0.32 0.85 0.41 0.49 0.35 0.59 0.49 0.29

CORR 0.90 0.16 0.83 0.97 0.85 0.95 0.83 0.90 0.88 0.90


USA

RMSE 0 0 0 0 0.02 0.05 0.01 0.04 0.06

mNSE 0.63 -0.42 0.75 -0.34 -3.93 -9.06 -0.44 -0.32 -2.62

md 0.82 0.41 0.86 0.43 0.19 0.09 0.51 0.43 0.22

CORR 0.97 0.79 0.99 0.87 0.41 -0.45 0.90 0.92 0.85

In the third row we can find the modified index of agreement (md), which is based on the indexof agreement (d).

1−∑T

t=1 (zt − zt)2∑Tt=1 (|zt − µz|+ |zt − µz|)2

When this statistic takes value 1, it implies that the data and the simulations coincide. As a result,the difference between them is 0, which reflect that the model can replicate the data perfectly.When this statistic is close to 0, it reflects that the simulations of the model are far from the data.Similarly to what happened in the previous statistic, it is affected by the scale of the data. Dueto the squares, differences of large values will be intensified, while differences of low values willbe reduced. The md statistic substitutes the square of the differences by their absolute value inorder to solve this problem.

md = 1−∑T

t=1 (|zt − zt|)∑Tt=1 (|zt − µz|+ |zt − µz|)

This statistic shows that the model successes in replicating the sectoral shares of labor forUSA, Tanzania and India. In terms of the relative aggregate productivity, this statistic reflectsthat the performance of the model is not so good.

The last row of the countries show the coefficient of correlation between countries. This statis-tic measures the linear relationship of two variables. In this case, indicates the relationship be-tween the observed and the simulated shares of labor. If it is positive, implies that both variablesmove in the same direction. This implies that the greater (lower) is the data, the larger (smaller)are its simulations. On the contrary, a negative sign reflects that variables move in different di-rections. This implies that when one variable is high the other is low and vice-versa. When thecoefficient is near to 1, data and simulations have a strong relationship. If the coefficient is near0, the relationship between data and simulations is weak.

Table 4.4 show that the relationship between the simulated changes in the sectoral shares oflabor and the observed ones is positive and high in cases like China, Egypt, Tanzania, India andthe USA. It is remarkable the case of Senegal. For this country, correlation between data andsimulations is negative in most sectors. Looking at the relative aggregate productivity, we canfind that this statistic takes high positive values for most countries.

Considering all the statistics, it is noticeable that the model replicates better the data of coun-tries that are in the first group. For Kenya and Tanzania the performance of the model is not sogood, but it is not as bad as in the remaining countries of groups 2 and 3.

Chapter 5

Counterfactuals

This analysis is based on several experiments. It will reveal the relevance of the sectoral produc-tivity growth on the aggregate productivity evolution of countries.Firstly, we analyze what has been the importance of each sectoral productivity on the labor alloca-tion and the relative aggregate productivity of countries. The experiments consist on replacing thesectoral productivity growth of countries by 0. As a result, we can obtain how would be the changein the labor allocation and the relative aggregate productivity when the productivity level of eachsector remains remains constant. The next step is to compare these changes to the ones estimatedfor the countries with their corresponding sectoral productivity evolution. This comparison willallow us to see how was the influence of each sectoral productivity on the aggregate productivityevolution of a country. Furthermore, we will analyze how sectoral productivity has affected theincome per capita evolution of each country.Secondly, we analyze the relevance of specific productivity paths. For this purpose, we substi-tute the sectoral productivity evolution of a country by the sectoral productivity evolution of othercountry initially similar to it, in income per capita terms. Comparing the estimated changes fora country in the relative aggregate productivity and income per capita we can observe whetherfollowing other paths it could have been better or not .

5.1 Role of the sectoral productivity growth of countries in theirrelative aggregate productivity and income per capita

Table 5.1 presents the estimated changes in the relative aggregate productivity and income percapita of groups, given the observed sectoral productivity paths of countries. In addition, we canfind how would have changed the sectoral labor allocation and the relative aggregate productivityof groups if, instead, some of the sectoral productivity of countries had remained constant1. It isnecessary to remark that experiments are done assuming that any of the other factors differentfrom the one analyzed do not change. This ensures that the results are only attributable to thefactor that is modified. Therefore, it can be appreciated what is the role played by the productivitygrowth of each sector in the sectoral labor allocation and the aggregate productivity of groups.

Changes in the relative aggregate productivity and the income per capita of groups are ex-pressed in percentage terms.

In this table, we can observe that there is a great difference on the change in the relative1The corresponding information on the sectoral shares of labor can be found in Appendix C

38


Table 5.1: Importance of the sectoral productivity growth in the evolution of countriesGroup 1 Group 2 Group 3

Aggr. Productivity GDPpc Aggr. Productivity GDPpc Aggr. Productivity GDPpcInitial 546.67 1411.03 8.77 98.29 -12.90 61.33

Estimations when each sectoral productivity growth is set to 0

AGR 190.52 597.59 -17.45 53.40 -48.98 -2.40MIN 458.10 1198.77 8.52 97.85 -13.03 61.13MAN 257.72 768.11 9.57 99.74 -6.79 72.55PU 531.95 1376.57 8.67 98.11 -12.64 61.80

CON 477.10 1245.86 11.72 103.44 -11.13 64.65WRT 421.74 1141.04 27.27 130.51 1.18 86.89TRA 441.12 1168.31 9.25 99.11 -11.01 64.75FIRE 476.47 1250.39 9.71 99.92 -11.52 63.79OTH2 268.22 750.77 21.05 119.56 2.02 88.51

aggregate productivity of groups when considering that the agricultural productivity is constantand equal to its initial value. Since the change in the relative aggregate productivity is much lowerwhen the agricultural productivity does not change, we may conclude that this sector has been oneof the main determinants in the aggregate productivity growth of all groups. It is remarkable theimportance of the productivity growth in agriculture for the second and the third group. If therehad not been any growth in the agricultural productivity, the relative aggregate productivity ofthe second group would have experienced a negative evolution. In the third group, the negativegrowth of the relative aggregate productivity would have even been four times greater. Therefore,we may conclude that the growth in the agricultural productivity has contributed positively to theevolution of the relative aggregate productivity of groups.

It can be appreciated that the change in the relative aggregate productivity of group 1 wouldhave been also lower without the increase in the manufacturing productivity or the personal andgovernment productivity. Keeping any of these productivity at their initial level, would not haveallowed the first group to reach more than half of the growth experienced in the relative aggregateproductivity. The changes in income per capita of this group also reflects these sectoral productiv-ity effects.

This table shows that the decrease in construction and in trade services experienced by group2 have affected very negatively to the evolution of its relative aggregate productivity. If the pro-ductivity of any of these sectors had not decreased, the relative aggregate productivity and theincome per capita of this group would have been much higher.

The initial estimations for group 2 differ from ones when the personal and government produc-tivity is kept constant. However, we can see that the average annual growth of the producitivityin the initial estimations is also 0 and the remaining factors do not change. This is because inthe first case, it is considered that both countries maintain constant their productivity, whereasin the second case, the countries considered experience very different growth rates, but, on av-erage, they are 0. Looking at the estimations for its members, we can find that the evolution ofthe productivity in the personal and government sector has been very important in their relativeaggregate productivity evolution. Indeed, if Ethiopia had not experienced any growth in the per-sonal and government productivity, the relative aggregate productivity of this country would haveexperienced a higher decreased. In the case of Malawi, if the country had maintained constant


this sectoral productivity, it could have achieved a much higher relative aggregate productivity.Therefore, we may conclude that the growth of the personal and government productivity is veryimportant in determining the evolution of the relative aggregate productivity of countries in group2.

The change in the relative aggregate productivity for group 3 would have been positive in-stead of negative, if its countries had not decreased their productivity in trade or personal andgovernment services. This would have implied also an increase in its income per capita change.

5.2 The importance of specific sectoral productivity paths

Table 5.2 shows the estimated changes in the relative aggregate productivity and income percapita for some countries over the period analyzed, given their sectoral productivity evolution. Inthe last column are presented the estimated changes in the income per capita of countries. Belowthese figures we can find what would have been the changes in those variables, if the country hadfollowed the sectoral productivity evolution of other countries or group of countries year by year2.

In this table, we can see that if India had followed the sectoral productivity evolution of theother countries in group 1, this country would have experienced a variation in the relative aggre-gate productivity that would have almost doubled its own change. Indeed, by only following theagricultural productivity growth of group 1, India could have achieved a noticeable increase inthe aggregate productivity. The productivity growth of mining experienced by group 1 alone couldhave also produced a greater change of the Indian aggregate productivity, though much lower thanthe produced by agriculture. Similarly, the income per capita of India would have experienced amuch higher rate if the country had followed the sectoral productivity paths of group 1. At a lowerextent, the income per capita of this country would have benefited from following the agriculturalproductivity growth of group 1. Much lower, but still positive, would have been if India had onlyfollowed the mining productivity path.

It can be appreciated that if Malawi had followed the sectoral productivity path of Egypt, itspositive change in the relative aggregate productivity would have been much higher. Lookingspecifically to several sectors, we can find that by following Egypt’s path in agriculture, Malawicould have achieved a greater increase in the relative aggregate productivity. This increase wouldhave been lower, if instead, Malawi had followed the manufacturing productivity path of Egyptonly. On the contrary, if Malawi had experienced the productivity path in services of Egypt, thecountry would have experienced a significantly higher growth rate in the relative aggregate pro-ductivity. The income per capita of Malawi would have had the same behavior than its relativeaggregate productivity when experiencing some of the changes in sectoral productivity describedpreviously.

When looking at how would have been Malawi if it had experienced Ethiopia’s sectoral produc-tivity growth, we find that it only would have been better, in terms of relative aggregate produc-tivity and income per capita, when considering Ethiopia’s services productivity path.

In the case of Ethiopia, it can be observed that the relative aggregate productivity changewould have been positive if Ethiopia had experienced the sectoral productivity path of Malawi.The change in relative aggregate productivity would have been much greater if Ethiopia had onlyexperienced Malawi’s agricultural productivity. However, the change would have been worse thanthe experienced by Ethiopia if the country had followed Malawi’s productivity growth in services.This is reflected on the estimations of the income per capita for Ethiopia. The greatest change is

2The corresponding information on the sectoral shares of labor can be found in Appendix C


Table 5.2: Consequences of following specific sectoral productivity paths

INDAgg.

ProductivityGDPpc

Initially 352.64 881.81With the productivity path of BWA, CHN and EGY in...

All sectors 661.72 1552.24AGR 478.09 1153.93MIN 358.65 894.84

MWIAgg.

ProductivityGDPpc

Initially 25.26 117.77With the productivity path of EGY in...

All sectors 703.70 1297.31AGR 62.25 182.09MAN 38.67 141.09

WRT-TRA-FIRE-OTH2

229.22 472.39

MWIAgg.

ProductivityGDPpc

Initially 25.26 117.77With the productivity path of ETH in...

All sectors -33.09 16.32AGR -44.61 -3.70

TRA-FIRE-OTH2

148.86 332.67

ETHAgg.

ProductivityGDPpc

Initially -7.71 78.82With the productivity path of MWI in...

All sectors 10.72 114.54AGR 37.62 166.65

TRA-FIRE-OTH2

-9.17 75.99

TZAAgg.

ProductivityGDPpc

Initially 76.18 215.70With the productivity path of KEN and SEN in...

All sectors -55.87 -20.93PU 77.81 218.62

WRT-TRA-FIRE-OTH2

77.73 218.47

TZA Agg.Productivity

GDPpc

Initially 76.18 215.70With the productivity path of Group 1 in...

All sectors 1455.52 2687.28PU 150.92 349.62

MIN-MAN 114.36 284.10WRT-TRA-

FIRE-OTH2491.83 960.49

KENAgg.

ProductivityGDPpc

Initially -35.14 23.66With the productivity path of Group 1 in...

All sectors 880.61 1769.72PU 35.18 157.74

MIN-MAN -19.40 53.69WRT-TRA-

FIRE-OTH256.09 197.61

SENAgg.

ProductivityGDPpc

Initially -79.75 -55.36With the productivity path of Group 1 in...

All sectors -30.69 52.81AGR 20.83 166.41

CHNAgg.

ProductivityGDPpc

Initially 1347.07 3164.61With the productivity path of BWA in...

All sectors 30.90 195.31AGR 145.65 454.18MIN 494.55 1241.32


estimated when Ethiopia follows only the agricultural productivity of Malawi. On the contrary,it is estimated that the change in income per capita would have been lower than the observed ifEthiopia had experienced the services productivity growth of Malawi.

Tanzania would have experienced a negative change in the relative aggregate productivity andthe income per capita if it had followed the sectoral productivity evolution of the other countries ofthe third group. If Tanzania had only followed the services productivity growth, the country wouldhave experienced increases significantly higher in these variables. On the contrary, following thesame productivity growth rates in utilities as the other members of group 3 would have producedsmall positive changes in the relative aggregate productivity and the income per capita of thecountry.

Kenya and Tanzania show a higher increase in their relative aggregate productivity and in-come per capita when following the sectoral productivity path of the first group. The countries ofthe third group would have seen a considerable increase in their change of relative aggregate pro-ductivity if they had experienced the sectoral productivity evolution of group 1. When consideringthat they follow the productivity of group 1 in specific sectors, it can be observed that changes arenot so great. In fact, the change in the relative aggregate productivity of Kenya is negative if thecountry only experiences the productivity growth of group 1 in industry. The greatest change isproduced when the countries follow the same services productivity path as the first group.

The relative aggregate productivity and income per capita of Senegal behave in differentlyfrom the other members of the third group. For this country, experiencing the same sectoralproductivity paths as the first group would have reduced the negative change in its relative ag-gregate productivity. However, it would imply a positive change in its income per capita. Senegalwould have experienced high positive changes in its relative aggregate productivity and incomeper capita if instead, it had only experienced the agricultural productivity of the first group.

With respect to China, it is noticeable that changes in its relative aggregate productivityand income per capita would have been much lower following the sectoral productivity path ofBotswana. This does not change much if we consider that China only follows the agricultural ormining productivity of Botswana.

Chapter 6

Conclusions

In this analysis, we have seen that there is not a single sector that explains the behaviour of theaggregate productivity and income per capita of groups 2 and 3. Both groups have decreased theirproductivity in most sectors. Similarly, there is not a single sector leading the evolution of group1. This group has been able to achieve positive growth rates in the productivity of all sectors.However, the counterfactuals show that there has been specific sectors that have influenced a lotin the relative aggregate productivity and income per capita growth of countries.Particularly, the experiments show that if the agricultural productivity had remained constant,the growth in relative aggregate productivity and income per capita of countries would have beenmuch lower.In addition, they reflect that the evolution of the personal and government services productivityhas influenced a lot in the evolution of the aggregate productivity and income per capita of coun-tries. If the productivity growth of this sector had been zero, countries in the first group wouldhave experienced approximately half of the increase in the aggregate productivity and income percapita. On the contrary, if the second and third group had maintained constant their productivityin personal and government services, they would have improved noticeably the changes in aggre-gate productivity and income per capita.The growth in the manufacturing productivity has affected very positively the relative aggregateproductivity and income per capita of group 1. If the productivity growth in this sector had been0, the growth of the relative aggregate productivity and income per capita of the first group wouldhave been reduced in half. This sector was also very important for group 3. If this group hadnot decreased its manufacturing productivity, it would not have decreased so much its relativeaggregate productivity and income per capita.The trade services sector has been very important for the second and third groups. The negativeevolution of the trade services productivity in these groups has impeded them to increase theirrelative aggregate productivity and income per capita as much as they could have done.

Looking at the individual experiments, we can appreciate that countries of group 3 wouldhave increased noticeably their relative aggregate productivity and income per capita if they hadfollowed the sectoral productivity growth of the first group. Indeed, by only following the agricul-tural or services productivity growth of the first group, they would have increased significantlythe change in their relative aggregate productivity and income per capita. Similarly, India wouldhave increased its relative aggregate productivity and income per capita much more if it had ex-perienced a sectoral productivity path more alike to the one of the other countries in group 1. Inthe case of Malawi, this country could have improved noticeably the change in relative aggregate

43


productivity and income per capita if it had experienced the sectoral productivity growth of Egypt.There are some cases in which following the sectoral productivity path of a country with greater

income per capita growth does not imply always an increase in the changes of relative aggregateproductivity and income per capita. This might be because the initial importance of sectors differsamong countries. This can be appreciated in the counterfactuals of Malawi with Ethiopia andTanzania with the third group.Malawi would have experienced a negative change in its income per capita and relative aggregateproductivity if it had followed Ethiopia’s productivity growth in all sectors or only in agriculture.However, if Malawi had only followed Ethiopia’s productivity growth in some services (transport,business and personal and government services) it could have increased much more its relativeaggregate productivity and income per capita.Tanzania would have experienced a negative change in its income per capita and relative ag-gregate productivity if it had followed the productivity growth of the third group in all sectors.However, if Tanzania had only followed their productivity growth in some services (utilities andtransport, business and personal and government services) it could have increased much more itsrelative aggregate productivity and income per capita.

The model used in this analysis assumes that countries allocate their labor force efficientlyamong all the sectors of the economy. The economies, in this model, are expected to devote agreater amount of their labor force to the sectors with greater productivity. However, mobilityacross sectors may not be so easy given that the skills of the labor demanded differ depending onthe activity. Therefore, the allocation of labor force in countries may not be always efficient.

It is beyond the scope of this article to determine the factors that underlie the changes in thesectoral productivity of countries, the sectoral productivity of countries is taken as an exogenousvariable. Therefore, we cannot conclude through this analysis that the causality between sectoralproductivity and the aggregate productivity or income per capita of countries goes in one direction.It might be that an improvement in economic conditions allows countries to redistribute theirresources and affect the sectoral productivity in future periods.

Another important aspect to keep in mind is that, had we included more countries in thesample, the greater the external validity of the study would have been. Analyzing more countrieswould allow us to ensure that the results we obtained could be applied to other countries thatwere not in our study but experienced an income per capita evolution similar to the ones describedpreviously. This is because we could prove that what we observe is not a singular case observedfor one country, but, on average, holds for a larger group. However, given the small number ofcountries studied in each group, we are aware that the results obtained from this analysis shouldonly be used to explain the evolution of the countries included on it.

Bibliography

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Costa, D.; Kehoe, T.J.; Raveendranathan, G. 2016. The Stages of Economic Growth Re-visited. Part 2: Catching Up to and Joining the Economic Leader. Economic Policy Pa-per. 16-6 (April 2016). Available at: https://www.minneapolisfed.org/research/economic-policy-papers/the-stages-of-economic-growth-revisited-part-2

Duarte, M.; Restuccia, D. 2010. The Role of the Structural Transformation in AggregateProductivity. The Quarterly Journal of Economics. 125 (1), pp. 129–173. Available at:https://doi.org/10.1162/qjec.2010.125.1.129

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McMillan, M.; Rodrik, D.; Sepulveda, C. 2017. Structural Change, Fundamentals, and Growth : AFramework and Case Studies. Policy Research Working Paper. 8041. World Bank, Washington,DC. Available at: https://openknowledge.worldbank.org/handle/10986/26481

Mamo, N.; Bhattacharyya, S.; Rabah Arezki, A.M. 2017. Intensive and Extensive Margins of Min-ing and Development: Evidence from Sub-Saharan Africa. OxCarre Working Papers. 189. Ox-ford Centre for the Analysis of Resource Rich Economies, University of Oxford. Available at:http://users.sussex.ac.uk/∼am401/research/MABM Mining.pdf

Park, C.Y.; Mercado, R.V. 2017. Economic Convergence, Capital Accumulation, and Income Traps:Empirical Evidence. TEP Working Paper. 1117 (April 2017). Trinity Economics Papers. Depart-ment of Economics, Trinity College, Dublin. Available at: https://ssrn.com/abstract=2993532

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Timmer, M. P.; de Vries, G. J.; de Vries, K. 2015. Patterns of Structural Change in DevelopingCountries. Handbook of Industry and Development (pp. 65-83). In J. Weiss, & M. Tribe (Eds.),Routledge. Available at: http://www.ggdc.net/publications/memorandum/gd149.pdf

45

https://www.minneapolisfed.org/research/economic-policy-papers/the-stages-of-economic-growth-revisited

https://www.minneapolisfed.org/research/economic-policy-papers/the-stages-of-economic-growth-revisited

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Appendix A

The decision problem of households

The first step to solve the decision problem of households is to analyze how they distribute theirconsumption among all the non-agricultural goods and services in order to minimize its cost. Al-ternatively, it can be obtained solving the following maximization problem:

max{ci}i≥0

ci =

(γ

1η

1 · cη−1η

1 + . . .+ γ1η

8 · cη−1η

8

) ηη−1


pi · ci = 1

To solve this problem we will use the Lagrange multiplier

L =

(8∑i=1

γ1η

i · cη−1η

i

) ηη−1

+ λ ·

(1− pa · ca −

8∑i=1

pi · ci

).

and differentiate it with respect to the different types of non-agricultural consumption

∂L∂ci

=η

η − 1·

(8∑i=1

γ1η

i · cη−1η

i

) ηη−1−1

· γ1η

i · cη−1η−1

i · η − 1

η− λ · pi = 0, ∀i = 1, . . . , 8

Those derivatives must be equal to each other and, through simple algebraic manipulation, we get

an expression for cjci

. Let R =8∑i=1γ

1η

i · cη−1η

i , and

∂L∂ci

=∂L∂cj

, ∀i, j = 1, . . . , 8 and i 6= j.

46


Then,

Rηη−1−1

· γ1η

i · cη−1η−1

i

pi=R

ηη−1−1

· γ1η

j · cη−1η−1

j

pj=⇒

γ1η

i · cη−1η−1

i

γ1η

j · (cj)η−1η−1

=pipj

=⇒

(cicj

)−1η

=pipj·(γiγj

)−1η

=⇒

cicj

=

(pjpi

)η· γiγj,

which gives uscjci

=

(pipj

)η· γjγi.

By considering the clearing condition for the labor market (equation 4.2), the production func-tion (equation 4.1), the clearing condition for the goods market (equation 4.3), the equation forthe relative non-agricultural consumption (equation 4.5) and the equation from the firm’s decisionproblem (equation 4.4) we get the following expression for the non-agricultural shares of employ-ment.

1 = Li + La +8∑

j=1, j 6=iLj =⇒

Dividing both sides by Li

1

Li= 1 +

LaLi

+

8∑j=1, j 6=i

LjLi

=⇒

Introducing the condition Yi = Ai · Li,

1

Li= 1 +

LaLi

+8∑

j=1, j 6=i

YjAiYiAj

=⇒

Because ca = Ya, ci = Yi,

1

Li= 1 +

LaLi

+8∑

j=1, j 6=i

cjAiciAj

.


Using the equation 4.5:

1

Li= 1 +

LaLi

+

8∑j=1, j 6=i

AiAj

(pipj

)η γjγi

=⇒

1

Li= 1 +

LaLi

+8∑

j=1, j 6=i

AiAj

(AjAi

)η γjγi

=⇒

1

Li= 1 +

LaLi

+

8∑j=1, j 6=i

(AjAi

)η−1 γjγi

=⇒

1 = Li + La +

8∑j=1, j 6=i

(AjAi

)η−1 γjγi

Li =⇒

γiAη−1i +

8∑j=1, j 6=i

γjAη−1j

Li = (1− La) γiAη−1i =⇒

Li =(1− La) γiAη−1

i

γiAη−1i +

8∑j=1, j 6=i

γjAη−1j

which gives us an expression for

Li =γiA


η−1i

.

Alternatively, this can be expressed as

1 = Li + La +

8∑j=1, j 6=i

(AiAj

)1−η γjγiLi =⇒

1 +8∑

j=1, j 6=i

(AiAj

)1−η γjγi

Li = 1− La =⇒

Li =1− La

1 +8∑

j=1, j 6=i

(AiAj

)1−η γjγi

.

Implementing the clearing condition for the goods and services market (equation 4.3) and theproduction function (equation 4.1), we can obtain an expression for the total consumption of non-


agricultural goods and services in terms of the sectoral employment.

C =

(8∑i=1

γ1η

i · cη−1η

i

) ηη−1

=⇒

Implementing the clearing conditions for the goods and services markets

C =

(8∑i=1

γ1η

i · Yη−1η

i

) ηη−1

=⇒

Implementing the production function

C =

(8∑i=1

γ1η

i · (Ai · Li)η−1η

) ηη−1

.

Substituting the expressions for the sectoral employment obtained previously we can express thetotal consumption of non-agricultural goods in terms of the labor force in the agriculture sector,which will help us to determine the consumption of agricultural goods.

C =

(8∑i=1

γ1η

i (AiLi)η−1η

) ηη−1

=⇒

Using equation 4.6

C =

8∑i=1

γ1η

i

Ai γiAη−1i (1− La)8∑i=1

γiAη−1i

η−1η

ηη−1

=⇒

Simplifying

C =

8∑i=1

γiAη−1i

1− La8∑i=1

γiAη−1i

η−1η

ηη−1

=⇒

C =

8∑i=1

γiAη−1i(

8∑i=1

γiAη−1i

) η−1η

(1− La)η−1η

ηη−1

.

Applying logarithms,

lnC =η

η − 1

ln

8∑i=1γiA

η−1i(

8∑i=1γiA

η−1i

) η−1η

+η − 1

ηln (1− La)

=⇒

lnC =

η

η − 1ln

7∑i=1γiA

η−1i(

8∑i=1γiA

η−1i

) η−1η

+ ln (1− La)

.


Secondly, for a given combination of consumption of non-agricultural goods, we can solve forthe optimal decision between the combination of all non-agricultural goods and the consumptionof the agricultural good. For this purpose, we will substitute the expression for the combination ofthe non-agricultural consumption in the household’s decision problem.

maxLa≥0

U = maxLa≥0

(1− a) · ln (ca − a) + a · ln[γ

1η

1 · cη−1η

1 + . . .+ γ1η

8 · cη−1η

8

] ηη−1

=⇒

Implementing the expression for the logarithm of the composite consumption

maxLa≥0

U = maxLa≥0

(1− a) · ln (ca − a) + a ·η

η − 1ln

8∑i=1

γiAη−1i(

8∑i=1

γiAη−1i

) η−1η

+ ln (1− La) =⇒

Implementing the clearing condition for the agricultural goods market (equation 4.3)

maxLa≥0

U = maxLa≥0

(1− a) · ln (Ya − a) + a ·η

η − 1ln

8∑i=1

γiAη−1i(

8∑i=1

γiAη−1i

) η−1η

+ ln (1− La) =⇒

Implementing the production function (equation 4.1)

maxLa≥0

U = maxLa≥0

(1− a) · ln (AaLa − a) + a ·η

η − 1ln

7∑i=1

γiAη−1i(

8∑i=1

γiAη−1i

) η−1η

+ ln (1− La) .

Now, we can solve for the optimal decision by differentiating with respect to the labor in agricul-ture and obtain an expression for it.

∂U

∂La=

(1− a) ·AaAa · La − a

− a · 1

1− La= 0 =⇒

(1− a) ·AaAa · La − a

= a · 1

1− La=⇒

(1− La) · (1− a) ·Aa = a · (Aa · La − a) =⇒

(1− a) = a · La + (1− a) · La −a · aAa

=⇒

La = (1− a) +a · aAa

.

Appendix B

Market clearing conditions

The expressions we have for the sectoral employment are:

Li =γi ·Aη−1

i · (1− La)∑i=1,...,8 γi ·A

η−1i

, for i = 1, . . . , 8.

From the labor market clearing condition we know that

1 = La +∑

i=1,...,8

Li.

Introducing our sectoral employment expressions

1 = La +

∑i=1,...,8 γi ·A

η−1i · (1− La)∑

i=1,...,8 γi ·Aη−1i

=⇒

1 = La +

∑i=1,...,8 γi ·A

η−1i∑

i=1,...,8 γi ·Aη−1i

(1− La) =⇒

1 = La + 1− La =⇒1 = 1.

51


The alternative expressions we have for the sectoral employment are:

Li =1− La

1 +8∑

j=1, j 6=i

(AiAj

)1−η γjγi

, for i = 1, . . . , 8.

From the labor market clearing condition we know that

1 = La +

8∑i=1, i 6=j

Li + Lj .

So, introducing our alternative sectoral employment expressions

1 = La +

8∑i=1, i 6=j

1− La + sA8

1 +8∑

j=1, j 6=i

(AiAj

)1−η γjγi

+

1− La −8∑

i=1, i 6=j

1− La

1 +8∑

j=1, j 6=i

(AiAj

)1−η γjγi

=⇒

1 = La + 1− La =⇒1 = 1.

Given that the clearing condition of the labor market is fulfilled in both cases, we can rely on ourexpressions for the sectoral employment.

Appendix C

Counterfactuals: changes in thesectoral shares of employment

The following tables show the changes in the shares of employment allocated to each sector bygroups. In addition, it presents how would be the changes if the productivity growth of each sectorhad been 0.

Group 1 LAGR LMIN LMAN LPU LCON LWRT LTRA LFIRE LOTH2

Initial -48.67 41.17 130.38 127.63 325.59 264.32 78.40 133.18 111.72AGR 0.00 -31.64 29.96 10.98 86.85 84.52 -19.98 24.97 -12.73MIN -48.67 491.97 102.96 102.05 278.62 216.10 57.81 112.38 82.21MAN -48.67 -11.08 273.43 40.90 148.16 143.52 3.73 63.36 13.20PU -48.67 38.56 126.09 574.48 316.60 256.93 74.79 129.11 107.06

CON -48.67 31.71 109.22 103.50 515.27 227.50 62.29 116.92 88.77WRT -48.67 18.97 111.46 93.44 252.76 468.23 48.29 105.06 73.43TRA -48.67 22.54 104.23 96.65 263.72 216.63 481.33 105.68 78.26FIRE -48.67 35.11 121.23 115.55 303.14 245.47 68.39 543.03 97.32OTH2 -48.67 -11.46 34.99 39.44 165.86 116.05 10.61 42.95 322.08


Initial -16.08 -15.30 12.60 -24.11 88.54 195.35 8.00 28.51 92.19AGR 0.00 84.14 0.28 -39.14 82.67 50.68 -46.28 -26.76 -23.88MIN -16.08 -2.11 12.49 -24.21 88.41 194.72 7.76 28.26 91.70MAN -16.08 -8.49 0.47 -21.98 95.04 200.35 9.78 30.98 94.60PU -16.08 -15.37 12.42 -2.12 88.26 194.84 7.81 28.29 91.84

CON -16.08 -10.19 19.28 -19.61 3.85 212.82 14.38 36.12 103.53WRT -16.08 4.16 45.58 -1.55 143.05 27.59 41.73 68.19 153.16TRA -16.08 -16.02 13.00 -23.78 89.08 197.48 -1.45 29.37 93.77FIRE -16.08 -15.28 12.89 -23.90 89.01 196.33 8.36 -1.67 92.87OTH2 -16.08 -18.24 26.47 -13.93 109.96 245.56 26.53 49.42 12.21

53



Initial -0.18 6.56 63.40 63.68 78.97 88.48 47.25 44.16 71.13AGR 13.06 -41.94 -31.88 -45.08 -4.58 -26.26 -47.70 -53.68 -34.47MIN -0.18 0.01 63.26 63.19 79.33 88.19 46.89 43.69 70.83MAN -0.18 15.22 6.40 72.99 93.27 100.43 55.97 52.13 81.81PU -0.18 6.79 63.90 0.53 79.37 89.08 47.76 44.69 71.68

CON -0.18 10.66 67.43 66.26 2.25 92.60 49.89 46.22 74.71WRT -0.18 24.06 91.73 93.00 108.51 17.85 73.43 70.14 101.21TRA -0.18 8.49 67.08 67.81 82.28 92.88 2.59 47.88 75.17FIRE -0.18 6.72 64.13 64.71 79.29 89.43 48.12 0.74 72.02OTH2 -0.18 26.47 92.38 91.71 112.27 121.55 72.69 68.70 17.68

The following table show the change in the share of labor allocated to each sector by somecountries. In addition, it presents which would have been the changes if the countries had followedthe sectoral productivity path of others.

LAGR LMIN LMAN LPU LCON LWRT LTRA LFIRE LOTH2

MWIInitial -39.12 -40.89 79.51 25.69 190.28 449.34 101.84 133.67 272.77

With the productivity path of EGY in...All sectors -63.29 261.01 355.56 713.43 357.99 495.97 292.72 531.83 253.66

AGR -63.29 -15.68 156.07 79.29 314.10 683.65 187.93 233.33 431.77MAN -39.12 -35.49 -16.44 37.16 216.78 499.48 120.26 154.99 306.79

WRT-TRA-FIRE-OTH2 -39.12 40.68 327.21 199.12 590.85 138.39 57.09 152.73 41.46With the productivity path of ETH in...

All sectors 6.96 69.74 -29.69 -59.85 33.59 -36.34 -78.20 -64.05 -82.15AGR 6.96 -88.95 -66.45 -76.51 -45.75 2.66 -62.28 -56.33 -30.34

WRT-TRA-FIRE-OTH2 -39.12 11.29 237.98 136.64 446.55 369.89 60.90 165.39 31.78ETH

Initial 6.96 10.29 -54.31 -73.91 -13.20 -58.64 -85.84 -76.64 -88.40With the productivity path of MWI in...

All sectors -38.51 -24.53 130.16 52.48 260.19 591.95 148.70 145.86 349.37AGR -38.51 1575.44 594.03 296.36 1218.67 528.37 115.17 254.90 76.22

TRA-FIRE-OTH2 6.96 -28.59 -70.42 -83.11 -43.80 -73.22 -79.67 -79.90 -63.27TZA

Initial -34.42 58.93 253.94 324.71 177.96 333.77 266.89 284.93 301.32With the productivity path of KEN and SEN in...

All sectors 6.50 -51.57 -50.30 -90.71 -48.80 -41.93 -71.80 -76.65 -61.71PU -34.42 60.11 256.56 -12.13 180.02 336.98 269.60 287.77 304.29

WRT-TRA-FIRE-OTH2 -34.42 55.51 246.32 315.57 171.98 433.60 159.15 114.59 251.83With the productivity path of group 1 in...

All sectors -57.82 182.84 471.85 421.81 723.65 634.55 315.03 487.26 356.67AGR -57.82 139.03 432.32 538.77 318.05 552.39 451.80 478.93 503.59

MIN-MAN -34.42 -51.59 -2.13 378.40 213.10 388.60 313.26 333.58 352.05WRT-TRA-FIRE-OTH2 -34.42 322.26 840.38 1028.42 638.52 196.55 67.55 137.08 84.36


LAGR LMIN LMAN LPU LCON LWRT LTRA LFIRE LOTH2

KENInitial -5.28 60.74 36.27 -33.69 158.95 31.68 -25.12 -52.43 12.06

With the productivity path of group 1 in...All sectors -57.75 67.67 239.00 209.34 388.28 335.45 146.04 248.14 170.72

AGR -57.75 335.77 269.44 79.77 602.02 256.97 102.99 28.95 203.80MIN-MAN -5.28 -86.21 -72.11 -19.84 213.04 59.18 -9.49 -42.50 35.47

WRT-TRA-FIRE-OTH2 -5.28 269.59 213.33 52.47 495.41 -31.87 -61.50 -45.53 -57.64SEN

Initial 39.17 -100.00 -100.00 -100.00 -100.00 -100.00 -100.00 -100.00 -100.00With the productivity path of group 1 in...

All sectors 39.17 -100.00 -100.00 -100.00 -100.00 -100.00 -100.00 -100.00 -100.00AGR -57.66 148.67 159.19 -77.18 57.29 264.90 60.32 64.49 85.55

MIN-MAN 39.17 -100.00 -100.00 -100.00 -100.00 -100.00 -100.00 -100.00 -100.00WRT-TRA-FIRE-OTH2 39.17 -100.00 -100.00 -100.00 -100.00 -100.00 -100.00 -100.00 -100.00

INDInitial -39.14 106.15 81.26 18.57 556.74 150.05 79.13 204.44 42.54

With the productivity path of BWA, CHN and EGY in...All sectors -61.92 7.47 177.83 186.45 200.52 255.62 82.49 149.12 121.74

AGR -61.92 167.20 134.94 53.69 751.22 224.10 132.18 294.60 84.75MIN -39.14 -32.43 83.36 19.95 564.33 152.94 81.20 207.96 44.19

CHNInitial -76.23 78.22 125.00 281.08 627.36 465.61 228.70 107.40 402.21

With the productivity path of BWA in...All sectors -16.71 -44.48 259.89 29.78 60.64 338.14 -29.91 103.27 -19.90

AGR -16.71 0.75 27.19 115.42 311.17 219.74 85.82 17.25 183.90MIN -76.38 417.53 309.45 593.46 1223.60 929.26 498.16 277.42 813.90

Remaining Poor or Growing at a High Rate: a Sectoral Analysis · Author: Belen Inguanzo Lorenzo´...

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